The Geometer’s Sketchpad
®
for TI-89, TI-92 Plus, and
© 2000-2002 KCP Technologies, Inc.
65
Voyage™ 200 PLT User Guide and Reference Manual
“through” the center point, and appears inverted on the opposite side of the
center.)
Reflection
Reflections create mirror-images of objects—objects are flipped across a
mirror, changing their orientation and location but not their size. In the
following illustration, the selected triangle is the image of the unselected
triangle reflected across the mirror segment DE.
The transformational parameter of a reflection is the mirror across which
the reflection flips. In Sketchpad, any segment, ray, line, or axis may act as
a reflection mirror.
The Mark commands (Mark Center, Mark Mirror, and so forth) are
used to establish transformational parameters before constructing
transformed images of selected pre-images. In general, each transformation
must be defined in terms of at least one marked parameter (required
marks). Some transformations may take advantage of additional marked
parameters (optional marks). You must mark the required parameters—and
any optional parameters you may be using—before choosing one of the
transformation commands (Rotate, Dilate, Translate, or Reflect).
To mark a transformational parameter, select appropriate objects to define
that parameter and then choose the corresponding Mark command, as
described in the following table. If you select more objects than 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 marked, it remains marked until you mark a different
object as that parameter or until you delete or undo the marked object(s).
For example, you need to mark a center only once in order to dilate or
rotate about that marked center many times.
If you attempt to transform a selected pre-image and have not marked a
required transformation parameter, Sketchpad will attempt to mark one for
you based on objects available in your sketch. (You’ll see a brief animation
indicating the marked parameter.) If no object exists that can be marked,
Sketchpad displays a warning indicating you must construct and mark the
appropriate parameter. For example, if you attempt to rotate without first
marking a point as center, Sketchpad will mark an existing point as center
before displaying the Rotate dialog box.
Mark Center
Mark Mirror
Mark Angle
Mark Ratio/Scale
Factor
Mark Vector
Mark Distance
Think of marking
parameters as similar to
selecting prerequisites for a
Construct command—
except marking is more
durable. Sketchpad
remembers parameters
you’ve marked until you
mark new ones—even if
they’re no longer selected.
Thus, you don’t have to
mark parameters again and
again each time you choose
a Transform command.
