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162 Geometry
Reflection A reflection is a
transformation which maps
an object or set of points
onto its mirror image, where
the mirror is either a point or
a line. A reflection through a
point is sometimes called a
half-turn. In either case, each
point on the mirror image is the same distance from the mirror
as the corresponding point on the original. In the example at
the right, the original triangle D is reflected through point I.
1. Tap and select
Reflection.
2. Tap the point or straight object (segment, ray, or line) that
will be the symmetry axis (that is, the mirror) and press
E.
3. Tap the object that is to be reflected across the symmetry
axis and press
E. The object is reflected across the
symmetry axis defined in step 2.
Dilation A dilation (also called a homothety or uniform scaling) is a
transformation where an object is enlarged or reduced by a
given scale factor around a given point as center.
In the illustration at the right,
the scale factor is 2 and the
center of dilation is
indicated by a point near the
top right of the screen
(named I). Each point on the
new triangle is collinear with
its corresponding point on
the original triangle and point I. Further, the distance from
point I to each new point will be twice the distance to the
original point (since the scale factor is 2).
1. Tap and select
Dilation.
2. Tap the point that is to be the center of dilation and press
E.
3. Enter the scale factor and press
E.
4. Tap the object that is to be dilated and press E.