The Geometer’s Sketchpad
®
for TI-89, TI-92 Plus, and
© 2000-2002 KCP Technologies, Inc.
64
Voyage™ 200 PLT User Guide and Reference Manual
cm vertically appears to the right (1 cm) and below
(2 cm) the pre-image.
Polar Vector
The translation vector is specified by a distance (by
which to translate) and an angle (the direction in
which to translate). An angular direction of 0° points
due east, and a direction of 90° points due north. An
image translated by a polar vector of 5 cm at 45°
appears above and to the right of its pre-image. (In
this polar vector example, the diagonal distance
between pre-image and image would be 5 cm.)
Marked Vector
The translation vector is specified by the previously
marked distance and direction between two points.
Thus if an object were translated by a vector from
point A to point B, where B was above and some
distance to the left of A, the translated image would
be defined above and to the left of its pre-image by
the same distance and direction.
Rotation
Rotations turn objects in the plane, affecting 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 illustration, the selected triangle is the image of the
unselected triangle dilated by a factor of one-half toward center point D.
The parameters of a dilation specify a center point, toward or away from
which the image contracts or expands, and a scale factor or ratio that
determines how much the image expands or contracts. If the magnitude of
the scale factor is less than 1, the image is smaller than the pre-image—a
ratio of 1/2, for instance, defines an image only half as big as its pre-image.
If the magnitude of the scale factor is greater than 1, the image is larger
than the pre-image—a ratio of 2/1, for instance, defines an image twice as
big as its pre-image. (If the scale factor is negative, the image is dilated
Positive angles result in
counter-clockwise rotations,
and negative angles result
in clockwise rotations.