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Key Curriculum Press Geometer's Sketchpad, User Manual And Reference Manual

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Getting Started

Introductory Tour

Customer Support

Advanced Tour

Using the Tools

Selection Arrow

Straightedge Tools

Point Tool

Text Tool

Compass Tool

Custom Tool

Using the Menus

Edit

Transform

Display

Measure

Construct

Graph

Tips and Techniques

Shortcuts

Construction Hints

Display Hints

Performance Tips

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Innovators in Mathematics Education

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Summary of Contents for Geometer's Sketchpad

Page 1: ...upport Advanced Tour Using the Tools Selection Arrow Straightedge Tools Point Tool Text Tool Compass Tool Custom Tool Using the Menus Edit Transform Display Measure Construct Graph Tips and Techniques Shortcuts Construction Hints Display Hints Performance Tips H H X XU UU UL LFX FXO OX XP P 3 3U UH HV VV Vë Innovators in Mathematics Education ti ...

Page 2: ... H H X XUU UUL LF FX XO OX XP P 3 3U UH HV VV Vë Innovators in Mathematics Education THE GEOMETER S SKETCHPAD for TI 89 TI 92Plus VoyageTM 200 UserGuideand ReferenceManual ...

Page 3: ...ometer s Sketchpad and Dynamic Geometry are registered trademarks of Key Curriculum Press Inc Sketchpad is a trademark of Key Curriculum Press Inc All other brand names and product names are trademarks or registered trademarks of their respective holders Copyright 2000 2002 by KCP Technologies Inc All rights reserved KCP Technologies Inc 1150 65 th Street Emeryville CA 94608 The Geometer s Sketchp...

Page 4: ...oint Tool 27 Compass Tool 28 Straightedge Tools 30 Text Tool 31 Custom Tool 34 Using Menus 40 ƒ Edit Menu 42 Display Menu 53 Construct Menu 58 Transform Menu 63 Measure Menu 69 ˆ Graph Menu 74 Shortcuts 81 Construction and Display Hints 84 Performance Tips 86 88 1 Introducing Sketchpad 2 Tools 3 Commands 4 Tips and Techniques Index ...

Page 5: ...nsions This sketch demonstrates a two point perspective view of a three dimensional cube In this perspective vertical edges of the 3 D cube remain vertical in its 2 D image but other edges recede toward one of two vanishing points on the image s horizon line Dragging the vanishing points alters the perspective dynamically Example from a TI 89 The circumcircle of a triangle This sketch starts with ...

Page 6: ...r constructions to see which properties change and which don t With Dynamic Geometry at your fingertips you can put the problems and theorems you encounter in your math class in motion revealing relationships and giving you a whole new way of seeing mathematics Try the following two Guided Tours for an overview of Dynamic Geometry and how to use Sketchpad on your TI 89 or TI 92 Plus Voyage 200 PLT...

Page 7: ... The Segment tool appears at the left of three pop up Straightedge tools Press to choose it Once the Segment tool is active the cursor becomes a cross hair 3 Press to construct a segment endpoint Press to move away from the first endpoint constructing a segment as you move Press again to construct the segment s second endpoint 4 Construct the first of two more segments to complete the triangle Wit...

Page 8: ...ets you generalize from a single construction For example in the steps above you drew a single triangle But by dragging you can look at many possible sizes and shapes for a triangle You can also drag to check that your construction is holding together properly that all possible appearances are still triangles Drag often Sketchpad s unlimited undo lets you look back at a previous state of your sket...

Page 9: ...e sketch area becomes blank again 2 Press Š TI 89 2 Š D to the Segment tool and press to choose the Segment tool Then press to construct a segment 3 Press Š TI 89 2 Š D until the Compass tool blinks then press to choose it 4 To construct a circle with this segment as radius move the Compass tool s cursor to one segment endpoint press Then press to start drawing a circle Position the cursor over th...

Page 10: ...d you notice that dragging one of the vertices didn t change the length of these equal sides What s different about that point You can automate dragging using animation Follow these steps to animate one vertex traveling around the circle Steps Display 1 Press N to deselect all objects Press on the point on the circle that does not change the circle s radius to select it If you re not sure you have...

Page 11: ... necessarily equal to another side Then press Construct Midpoint 2 In order to construct a perpendicular line through this midpoint you ll have to select two objects a point to go through the midpoint in this case and a straight object to be perpendicular to the base segment in this case The just constructed midpoint is already selected Select the base segment as well by moving the Arrow to it and...

Page 12: ...h you select them The second middle point you select will be the vertex of the angle you re about to measure 2 Press Measure z Angle to measure the angle 3 Press N to deselect all then select the three vertices of the triangle again with your second selection a different point than the second selection you made in step 1 4 Press Measure z Angle to measure this second angle 5 Press N to deselect al...

Page 13: ... around the circle 4 To stop the animation Press Display Ñ Stop Animation TI 89 j A 5 While the point on the circle is selected Press ƒ Edit y Split Point From Circle Split From Object on the TI 89 The point is redefined to be no longer on the circle 6 Drag the point to confirm that it s no longer related to the circle Now that the point is no longer on the circle what kind of triangle do you have...

Page 14: ...oint tool from the toolbox Š TI 89 2 Š 6 Move the cursor to one side of the line and press to construct a point nearby 7 With the point still selected Press Transform Ñ Reflect TI 89 j A Sketchpad constructs and displays the image of your point reflected across the marked mirror 8 Press N to return to the Arrow then drag either point to see how its mirror image behaves Try dragging the mirror and ...

Page 15: ... and a unit point to the right of the origin To shrink the axes scales press N to deselect all then drag the unit point toward the origin Drag it just until you can see the 5 on the x axis 4 Press N to deselect all then press on each of the three triangle vertices Press Measure Analytic TI 89 jD Ú Coordinates 5 Press N to deselect all then press on the mirror line Press Measure Analytic TI 89 j D ...

Page 16: ...each one has 0 as one of its coordinates Describe where you located the points 5 See if you can locate the three vertices of the triangle so that one vertex is at the origin and each of the two other vertices has 0 as one of its coordinates Describe where you located the points and describe the triangle 6 Locate the mirror line so that its equation is y 2x See if you can locate the base vertices s...

Page 17: ... origin with each base vertex on an axis The triangle is a right isosceles triangle 6 This is tough The midpoint of the base is the point where the base intersects the mirror line The base vertices will both be grid points if and only if this midpoint is a grid point So locate a point on the grid that the mirror line passes through such as 0 0 1 2 2 4 and so on Try to position a base vertex so tha...

Page 18: ...ur sketch See the Tools chapter for more detail about tools Choosing a Tool Press Š TI 89 2 Š to enter the toolbox Use the cursor controls to highlight the tool you wish to use Press to choose a highlighted tool Alternately use the keyboard shortcuts ƒ ˆ TI 89 to activate tools directly The number of the shortcut corresponds with the position of the tool for example the Compass tool which is the t...

Page 19: ... s over an object the cursor will turn into a horizontal arrow Press and hold down TI 89 j as you move the object with See the Commands section for more details about using menu commands Sketchpad s six menus are ƒ Edit Display Construct Transform Measure and ˆ Graph Selecting To act on objects using menu commands you ll need to select them 1 Choose the Arrow tool 2 Using the cursor controls posit...

Page 20: ...Menu The Display menu TI 89 Use these commands to hide and show objects and their labels to trace objects and to animate objects The Construct Menu The Construct menu TI 92 Plus Voyage 200 PLT This menu provides a large assortment of Euclidean constructions as well as interiors and loci Some of these commands construct the same objects as some of the tools Others are shortcuts for commonly perform...

Page 21: ...alytic geometry environment as well as explore many of the connections between geometry and algebra Once you ve started to get the hang of making and acting on basic geometric figures you can use the Display menu to make action buttons Action buttons can hide show and automatically move objects in your sketch turning it into a presentation that someone else can interact with and learn from See Act...

Page 22: ...s arc constructions used to balance the serifs small tails of the character R The character itself is constructed in Sketchpad as a polygon interior where the polygon R has many hidden vertices Today s computers perform similar constructions thousands of times a second generating polygons from mathematical definitions to display as alphanumeric characters A presentation of the Pythagorean Theorem ...

Page 23: ...described here Steps Display 1 Press Š TI 89 2 Š to enter the toolbox The active tool begins blinking 2 Move to the desired tool Press C and D to change active blinking tools 3 Some tools have a palette of choices which appear to the left of the tool A and B move through the palette of choices Using Tools The toolbox appears on the right side of the screen and displays the available tools The acti...

Page 24: ...the view of the plane to the right scrolling objects visible in the view to the left You may reposition the view at any time regardless of which tool is active in the toolbox 1 ƒ TI 89 1 activates the first tool the Arrow without having to enter and leave the toolbox TI 89 2 activates the second tool the Point tool and so forth For a tool with a palette of choices such as the Straightedge tools pr...

Page 25: ...d 5 Repeat steps 2 through 4 to select additional objects Selection Arrow Tools This section describes the Selection Arrow tools which you ll use to select and drag objects Selecting objects is an important technique for using Sketchpad s menu commands Dragging objects to explore properties of a construction under a variety of transformations is the heart of Dynamic Geometry About the Selection Ar...

Page 26: ...to the opposite corner of the objects you wish to select Sketchpad displays a selection marquee rectangle between the two corners 4 Release TI 89 j Every object inside the marquee or intersecting the marquee becomes selected For convenience Sketchpad deselects previous selections when starting a new marquee Press and hold 2 before beginning a marquee to prevent this deselection that is to create a...

Page 27: ...ect Related objects adjust automatically Dragging an object with the Dilate Arrow dilates that object toward or away from the point currently marked as center Dilation changes the size but not the orientation of an object as you dilate toward the marked center the dragged object s becomes smaller as you dilate away from the marked center the object s becomes larger Related objects adjust automatic...

Page 28: ...on the Point tool on top of another object such as a segment or a circle before pressing The object will appear highlighted when you point to it indicating that the Point tool is ready to construct a point on it To construct points of intersection position the Point tool at the intersection of two objects such as a segment and a circle before pressing The objects will appear highlighted when the c...

Page 29: ...e second point As mentioned in steps 2 and 4 the Compass tool may be positioned over an existing point over blank space over a path or over the intersection of two objects If the Compass is positioned over an existing point Sketchpad uses that point to define the circle s center or radius point as the case may be in other words it doesn t construct a new point there If the Compass is positioned ov...

Page 30: ...o create a circle with center A and radius point B This circle is defined as centered at point A and passing through point B Moving B will change the circle s radius Imagine however that you had pressed the second time in a blank area thus constructing point C as shown at right in such a way that the circle appeared to pass through point B In this case moving B will not change the circle s radius ...

Page 31: ... Segment tool requiring two points to define a ray The first point determines the start or initial point of the ray The ray passes through the second point and continues infinitely far in that direction The Line tool acts like the Segment tool requiring two points to define a line These points determine the line s direction and the line extends through them infinitely far in each direction Straigh...

Page 32: ... Sketchpad creates a default label based on the type of object it names and the order in which it is displayed The next section describes how to change an object s default label Type of Object Label Sequence 1 Points A B C 2 Segments Rays Lines j k l 3 Circles c1 c2 c3 4 Polygon interiors P1 P2 P3 If an object s defining points are labeled but the object itself has not yet been labeled any measure...

Page 33: ...el You can drag the label a small distance around the object s perimeter but Sketchpad prevents you from dragging it too far 3 Release TI 89 j Captions are blocks of text that are not associated with specific objects Add captions to your sketches to give them titles or to explain your constructions Steps Display 1 Using the cursor controls point the Text tool at blank space away from all objects o...

Page 34: ...isting text of labels captions or measurements Steps Display 1 Using the cursor controls point the Text tool at existing text The tool changes its appearance when pointing at editable text a small A appears 2 Press Sketchpad opens the Properties or Edit Caption dialog box for the indicated object 3 Edit the existing text 4 Press twice to close the dialog box Sketchpad updates the edited text Chang...

Page 35: ...ion may be divided into three groups The independent objects or givens are objects that are necessary for the construction but that are not defined by the construction The dependent objects are objects that are defined by the givens or by other dependent objects in the construction These dependent objects may be divided into results which are the objects of ultimate interest in the construction an...

Page 36: ... available means such as existing tools and commands from the Construct Transform Measure and Graph menus Before creating your tool drag objects in the example construction to verify that it s correct Example Construction Perpendicular Bisector 1 In a new sketch use the Segment tool to create a new segment 2 With the segment selected Press Construct Midpoint Sketchpad displays and selects the midp...

Page 37: ...s Choose Create New Tool from the menu 6 Sketchpad presents a dialog box asking you to name your new tool Type PerpBisector and press twice to close the dialog box Congratulations You have just created and named your first custom tool To try out this tool immediately continue to the next section For additional information on creating other custom tools skip to More About Tools next page To activat...

Page 38: ...because you selected two points as givens when defining the tool In general the objects required by the tool correspond to the objects you selected as givens when defining it in the order in which you selected them 1 Try using the PerpBisector tool but place the endpoints of the perpendicular bisector on existing points Like the built in drawing tools your custom tools can place independent endpoi...

Page 39: ...reated or to save collections of them as toolkits and reopen saved tools from existing toolkits By saving collections of tools as toolkits you can distribute tools you create to others using VAR LINK See the guidebook for your handheld device at education ti com guides for instructions on using VAR LINK to transmit saved toolkit variables between graphing calculators Once a tool has been defined i...

Page 40: ...ine through B at point C When A and B are animated at the same speed C travels along the sine wave The shaded image is the trace of segment BC as both points animate slowly How long would the original horizontal segment have to be in order for the sine curve to trace exactly one wave period A fishy tessellation Periodic tessellations are geometric patterns that when repeated fill the plane A start...

Page 41: ...by simply pressing Besides the numbers and letters assigned to menu commands you ll see icons and symbols next to some commands These are explained below Padlocked Commands A padlock icon Πnext to a command indicates that the command is not available at the moment because the objects required by the command have not been selected in the sketch For example Construct Midpoint will be padlocked unle...

Page 42: ... press Transform n Rotate Sketchpad presents a dialog box in which you can enter an angle of rotation Commands with Submenus Commands that appear with before the command name and ú at the right edge of the menu have submenus of additional commands associated with them For example if you press ƒ Edit o Sketch you ll open a submenu from which you can press New Open or ª Save You can invoke certain m...

Page 43: ... calculator memory Sketchpad refreshes its Undo history whenever you reopen a saved sketch To save and reopen a sketch while working on it thereby refreshing the Undo history press ƒ Edit o Sketch Open and then press to indicate that you do want to save changes before closing Type the name of the sketch either a new name if this is the first time this sketch has been saved or the previously entere...

Page 44: ...later be split Splitting Points from Objects To separate a point constructed on an object such as a point on a segment a midpoint or an intersection from that object select the constructed point and choose Split Example Splitting a Point from a Segment 1 Select a point constructed as a Point on Segment or as a Midpoint of a segment 2 Press ƒ Edit y Split Point From Segment Split From Object on the...

Page 45: ...the point using Point on Object see page 58 Example Merging a Point to an Object 1 Select an independent point and a path in this case a circle 2 Press ƒ Edit y Merge Point to Circle Merge to Path on the TI 89 The point moves to merge with the path Merging Text To merge separate pieces of text together into a single sentence select one or more captions as well as any measurements or other text obj...

Page 46: ...nts Select Children selects the objects that are geometrically defined by the current selected objects Use this command to determine the set of objects that were constructed from a given selected object Before After Select Children does not change the selection if the currently selected object has no children Properties allows you to change a variety of properties of the selected object Select a s...

Page 47: ...ll of the parents of the selected object that is all objects that geometrically define the selected object No parents will appear if the selected object is independent Choose a parent from the menu to switch to the Properties dialog box for that parent Children This pop up menu lists all of the children of the selected object that is all objects that are geometrically defined by the selected objec...

Page 48: ... Properties This page contains properties about a measurement s display It appears only when a measurement or calculation is selected Prefix This text appears before the value of a measurement Sketchpad sets it by default to indicate the geometric property being measured but you can replace it with other text Suffix This text appears after the value of a measurement By default Sketchpad leaves it ...

Page 49: ... connects all of a locus s sampled points into a curve When discrete Sketchpad displays the locus s samples as individual points and does not connect them Continuous Sample Points Discrete Sample Points Graph Properties This page contains properties about graphs of functions It appears only when a function plot is selected See Plot Function page 78 for more information about function plots of Samp...

Page 50: ...hows By default Sketchpad shows all objects as Selected If you would rather the Show button not select the objects that it shows switch this property to Deselected Button Properties for Animate Buttons The properties for Animate buttons give you control over the various animated points that are set in motion by the button when it is pressed See Animate page 55 for a discussion of animation Options...

Page 51: ... New Press ƒ Edit o Sketch New to close the current sketch and create a new blank sketch If the previous sketch has been changed since it was last saved Sketchpad asks if these changes should be saved before creating a new sketch Use New when you wish to start an entirely new diagram or construction Open Press ƒ Edit o Sketch Open to close the current sketch and open a previously saved sketch or a...

Page 52: ...de settings that take effect immediately Others such as Text Sizes determine how new objects are created and therefore don t take effect until you create new objects Use the function keys ƒ at the top of the Preferences dialog box to choose different Preference pages Text Preferences Text Sizes Determines the size of text for newly created object labels action buttons captions or measurements Choi...

Page 53: ...t when displaying a new locus of points The greater the number of samples the more accurate the depiction of the locus and the smoother its appearance on the screen However the greater the number of samples the slower Sketchpad will be in calculating and displaying the locus Function Plots Determines how many samples Sketchpad will plot when displaying a new function plot Display Determines how Sk...

Page 54: ...isplay Hiding an object s label never changes that label Show Labels and Hide Labels are available only when you have selected objects for which labels can be displayed Most geometric objects can display labels but objects like measurements and captions do not display additional labels The Line Width settings Thin and Thick determine the appearance of selected circles segments rays lines axes poin...

Page 55: ...will leave behind traces when it s moved 3 Drag any part of your construction that causes the previously selected object to move Sketchpad displays traces of that object s former locations 4 To stop tracing the traced object select it again and press Display to show the menu Trace now appears with a checkmark indicating that tracing is activated for the selected object Press Trace to deactivate tr...

Page 56: ...hs For instance a point constructed on a circle animates at a constant rate around the circle See Point on Object page 58 for more information about points defined on paths 3 Other objects animate by moving the parental points that define them These points will be independent points points defined on paths or a combination of the two Animate is available only when one or more geometric objects are...

Page 57: ...ecause N switches to the Arrow if the Arrow is not active or deselects objects if any objects are selected pressing N repeatedly will eventually stop an active animation The Action Buttons menu creates action buttons in your sketch When pressed with the Arrow tool these buttons perform actions similar to those that could be performed using menu commands Use action buttons to make frequently used c...

Page 58: ...e one or more points directly to specific destinations specified by other points in the sketch To create a Move button select a point to move and a second point as its destination If you want to move more than one point continue selecting pairs of points the first to move the second as destination Then press Display Ò Action Buttons TI 89 j B ª Movement Sketchpad creates a Move button and then dis...

Page 59: ...ircle Locus of Points Function Plot Along the object 2 Polygon Interior Along the polygon s perimeter 3 Circle Interior Along the circle s circumference To construct the midpoint of a segment first select a segment Then press Construct Midpoint Sketchpad constructs and selects the midpoint of the selected segment To construct multiple midpoints simultaneously select multiple segments Before After ...

Page 60: ... direction in that order Then press Construct z Ray Construct more than one ray at a time by selecting three or more points before choosing Construct z Rays To construct a line select two points through which the line should pass Then press Construct Line Construct more than one line at a time by selecting three or more points before choosing Construct Lines To construct a parallel line select a p...

Page 61: ...point perpendicular to two or more straight objects select the given point and two or more straight objects Then press Construct n Perpendicular Lines Perpendiculars on the TI 89 To construct an angle bisector select three points defining the angle to bisect Select the vertex of the angle second Then press Construct o Angle Bisector Before After To construct a circle select two points The first se...

Page 62: ...d interior of various objects Its name changes based on the current selection Polygon Interior To construct a polygon interior select three or more points as vertices of the polygon in consecutive order Then press Construct Ó Polygon Interior Before After Note that the order in which points are selected determines the shape of the polygon interior Selecting Five Points One Way Selecting Them Anoth...

Page 63: ...7 If a point locus is infinitely large as it may be if the path of the driver point is infinitely long Sketchpad will display a finite portion of the locus with arrowheads to suggest that it continues infinitely far Alter the displayed portion of the infinite locus by dragging the arrowheads with the Arrow tool Dragging arrowheads in the direction their arrow points makes the displayed portion of ...

Page 64: ...escribed in more detail in the following sections Translation Translations slide objects in the plane without turning them their location is affected but not their size or orientation In the following illustration the selected triangle is the image of the unselected triangle translated by some distance to the right The parameters of a translation specify a vector indicating how far and in which di...

Page 65: ...cting their location and their orientation but not their size In the following illustration the selected triangle is the image of the unselected triangle rotated by 90 about center point D The parameters of a rotation specify a center point about which the image turns and an angle of rotation Dilation Dilations expand and contract objects affecting their size and location In the following illustra...

Page 66: ... necessary Sketchpad will mark the most recently selected object as the parameter For instance Mark Center requires that you select a point to mark as the center for subsequent rotations or dilations If more than one point is selected Mark Center will mark the most recently selected point as center Sketchpad confirms the Mark command with a brief animation of the marked object Once a parameter is ...

Page 67: ...on scale factor is equal to the ratio of segment lengths j k y Mark Ratio Three collinear points selected in order A B C Optional ratio of dilation scale factor is equal to the ratio of the directed lengths AC AB this ratio is negative if B and C are on opposite sides of A y Mark Scale Factor One scalar measurement a measurement with no units Optional scale factor of dilation z Mark Vector Two poi...

Page 68: ...r the distance you may choose between a previously marked distance and a fixed distance such as 5 cm For the direction you may choose between a previously marked angle and a fixed angle such as 45 Rectangular To enter a rectangular vector a vector specified by horizontal and vertical offsets For these offsets you may choose between previously marked distances and fixed distances such as 5 cm Marke...

Page 69: ...e previously see Mark Angle page 65 Press to complete the rotation To construct the dilated image of an object or objects first mark a point as the center of dilation see Mark Center page 65 Then select the pre image object s and press Transform o Dilate Sketchpad displays the Dilate dialog box In the dialog box enter the ratio of dilation You may enter a constant ratio such as 1 2 or a marked rat...

Page 70: ...t ª Perimeter One or more polygon interiors Perimeter of polygon s y Circumference One or more circles or circle interiors Circumference of circle s z Angle Three points selected in order A B C Measure of angle ABC vertex is second selected point Area One or more circles circle interiors or polygon interiors Area of circle s or polygon interior s m Arc Angle One circle and two or three points on t...

Page 71: ...ividual measurement at any time by editing its Measure Properties see page 47 Value The value of a measurement changes if the measured property changes as you drag or animate an object Measurement values are displayed in the current units set in Preferences See Preferences page 51 for information on changing units Prefix The prefix of a measurement is text displayed before the measurement Sketchpa...

Page 72: ...ys the result in your sketch When entering an expression you may correct mistakes by using A and B to move the insertion point Press A or B to move the insertion point to the beginning or end of the calculation Press 0 to remove the term immediately to the left of the insertion point or 0 to remove the term immediately to the right of the insertion point If you press when an invalid expression is ...

Page 73: ...scribed in the ˆ Graph menu section If no coordinate system is active when you make an analytic measurement Sketchpad creates a coordinate system for you Coordinates To measure the coordinates of a point or points select the point s and press Measure TI 89 j D Ú Analytic Coordinates Sketchpad measures and displays the coordinates of the selected point s Before After Unlike other measurements coord...

Page 74: ...sa X Sketchpad measures and selects the abscissa of the selected point Ordinate Y To measure the ordinate or y coordinate of a point select that point and press Measure TI 89 j D ÚAnalytic y Ordinate Y Sketchpad measures and selects the ordinate of the selected point Of course you can see both the abscissa and ordinate of a point together when you measure that point s coordinates But you may somet...

Page 75: ... origin in the coordinate system s units and θ measures the signed angle that a ray from the origin through the point makes with respect to a ray extending from the origin to the right Coordinate systems contain the following components Origin Axes Unit Point Grid Origin A point that defines the center of the coordinate system Drag the origin to change the coordinate system s location in the plane...

Page 76: ...t select to define them Command Selection Result Define Origin One point Square coordinate system centered on the selected point and with a default unit Define Unit Circle One circle Square coordinate system centered on the selected circle and with a unit equal to the circle s radius Define Unit Distance TI 89 Define Unit One segment or one distance measurement Square coordinate system with a defa...

Page 77: ...polar shapes Note that if you have defined the active coordinate system in terms of a single unit length for instance by Define Unit Distance or Define Unit Circle you can switch it between square and polar shapes but you cannot switch it to a rectangular shape because rectangular coordinate systems must be defined by two unit lengths Similarly if you have defined a coordinate system in terms of t...

Page 78: ...se steps 1 Select two measurements or calculations the first defining an x coordinate the second defining a y coordinate 2 Press ˆ Graph TI 89 2 ˆ Plot As x y Sketchpad constructs a point whose rectangular coordinates are equal to the two selected measurements Changing the values of the measurements by altering the geometric properties they measure changes the coordinates of the point Or on a pola...

Page 79: ...he calculator entry line but you can change it with the Graph menu 3 In addition to measurements the ƒ Values menu includes your function s independent variable for entry into your equation You can also type the independent variable from the keypad Change independent variables with the Graph menu Example Graph y 2x 1 Display 1 Press ˆ Graph TI 89 2 ˆ m Plot Function Sketchpad displays the function...

Page 80: ...ed on them but cannot be intersected transformed or measured You can alter the interval over which Sketchpad evaluates the function by dragging the arrowheads that appear at the plot s endpoints with the Arrow tool or by specifying the domain of the independent variable numerically using Graph Properties see page 48 Recall that Sketchpad evaluates certain trigonometric functions in the current uni...

Page 81: ...oscillating spiral about the origin In this sketch k is the angle formed by a point on a circle the circle s center and a second point on the circle Tracing the function plot as one of the points on the circle animates around the circle graphs a family of curves related by rotation Dilating a polar graph This sketch is based on the graph of r sin 6θ 2 with θ interpreted in radians Dilating a point...

Page 82: ... immediately Š hides the toolbox if it is showing or shows the toolbox if it is hidden see Show Hide Toolbox page 57 for more information TI 89 keystrokes TI 92 Plus Voyage 200 PLT keystrokes Effect Z Z ƒ Edit Undo command X X ƒ Edit Redo command 0 0 ƒ Edit ª Delete command A A ƒ Edit z Select All command P c ƒ Edit Select Parents command C d ƒ Edit m Select Children command O O ƒ Edit n Propertie...

Page 83: ...ing a Selection Arrow tool at an intersection of two objects constructs and selects the point of intersection 2 2 when using a drawing tool Point tool Compass tool etc prevents previously selected objects from deselecting you can either press and hold down the 2 key while using the tool or you can press and release the 2 key immediately before pressing the first or in the case of the Point tool on...

Page 84: ...oth the TI 89 and the TI 92 Plus Voyage 200 PLT The action taken by N depends on your current activity but if you press N repeatedly eventually you will return to a sketch in which the Translate Arrow is the active tool no objects are selected no animation is active and no traces are visible Specifically pressing N 1 Closes a pulled down menu without choosing any command in it if a menu is showing...

Page 85: ... a segment that is exactly 3 cm long While you could create a segment with the Segment tool measure its length and drag the segment s endpoints until the measurement was exactly 3 cm this segment would not be constructed to be exactly 3 cm long That is nothing in your definition of the segment indicates that it must remain 3 cm in length and when you drag it its length will change To fix a distanc...

Page 86: ...two ways to show just one or a few hidden objects The first is to use ƒ Edit n Properties to set the visibility of a hidden object to show it While you cannot select a hidden object to display its Properties directly you can select a related object a parent or a child of the hidden object and then navigate to the hidden object s Properties using the Parents and Children menus in the Object Propert...

Page 87: ...when placing multiple selected points to use the key instead of the M key shortcut in order for the 2 key to have the desired effect Then repeatedly alternate between the Segments command and the Midpoints command from the Construct menu without changing your selections between commands The final figure can be constructed in just a few seconds Loci and function plots are the most complex objects t...

Page 88: ...raphing calculator hiding the grid may also improve the legibility of your sketch Keep in mind that Sketchpad supports unlimited undo and redo of basic operations see page 42 Though very powerful unlimited undo has a cost it uses program memory to remember every basic action you ve performed in your sketch Thus whenever you delete objects in a sketch see Delete page 43 Sketchpad deletes them from ...

Page 89: ...mation 65 children 46 Circle By Center Radius 61 Circle Interior 61 circles by center and radius 61 constructing 28 Circumference 69 Clear All Traces 54 Commands 39 Compass Tool 28 Construct menu 58 Construction Hints 84 coordinate systems 74 defining 75 graph form 76 grid visibility 76 grids 87 marking 76 plotting functions 78 plotting points 77 polar 76 rectangular 76 snapping 76 square 76 coord...

Page 90: ...equences 31 showing 31 53 Large text size 54 Length 69 Line 59 Line Tool 30 Line Width 53 lines 59 parallel 59 perpendicular 60 loci continuous 48 discrete 48 number of samples 48 preferences 52 properties 47 Locus 62 Locus Properties 47 Mark Angle 65 Mark Axes 76 Mark Center 26 65 Mark Coordinate System 76 Mark Distance 65 Mark Mirror 65 Mark Ratio 65 Mark Scale Factor 65 Mark Vector 65 marks ang...

Page 91: ...splitting from objects 43 polar coordinates 74 Polar Grid 76 Polygon Interior 61 Preferences 51 Properties 45 radians 52 Radius 69 Ratio 69 ratios of dilation 65 Ray 59 Ray Tool 30 rays 59 angle bisectors 60 rectangular coordinates 74 Rectangular Grid 76 Redo 42 Reflect 68 reflection 65 repositioning the view 23 results 34 Resume Animation 55 Rotate 68 Rotate Arrow 26 rotation 64 Save 51 scaling 6...

Page 92: ...ctive tool 22 choosing 22 Compass Tool 28 Custom Tool s 34 Dilate Arrow 26 Line Tool 30 Point Tool 27 Ray Tool 30 Rotate Arrow 26 Segment Tool 30 Selection Arrows 24 shortcuts 23 stopping 83 Straightedge Tools 30 Text Tool 31 Translate Arrow Tool 26 using 22 Tours Advanced 13 Introductory 6 Trace 54 traces clearing 83 Transform menu 63 transformations angles 65 centers 65 dilation 64 68 distances ...

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