d. Unfold the patty paper and label the vertices asD[U+0080][U+0099],E[U+0080][U+0099],andF[U+0080][U+0099],
the image points of theD,E,andF.
e. Darken in the fold – this is the reflecting line. Label a point on this lineQ.
f. Use a ruler to drawF F′. Mark the intersection of the reflecting line andF F′pointM.
g. Measure theF MandF[U+0080][U+0099]M. What do you notice about these distances?
h. Measure^6 F MQand^6 F[U+0080][U+0099]MQ. What do you notice about these measurements?
Extension - Reflections and Translations!Use the diagram below. Reflect 4 CATover line m, obtaining 4 C[U+0080][U+0099]A[U+0080][U+0099]T[U+0080][U+0099].
Now reflect 4 C[U+0080][U+0099]A[U+0080][U+0099]T[U+0080][U+0099]over linen, obtaining 4 C[U+0080][U+009D]A[U+0080][U+009D]T[U+0080][U+009D].
The resulting image is a translation of the preimage, double the distance between the parallel lines.
Rotations
Pacing:This lesson should take one class period
Goal:Rotations are also an important concept in geometry. Tires rotate in 360 degree increments, as do the hands
on a clock. This lesson presents the concept of rotations and how matrix multiplication is used to compute the image
points.
Extension – Reflections and Rotations!Just as translations are a composite of reflections over parallel lines, rotations
are a composite of reflections. The only difference is that rotations occur when the reflecting lines intersect. Have
your students complete the following:
Using the diagram below, reflectABCDover linef, resulting inA[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099]D.
ReflectA[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099]D[U+0080][U+0099]over linee, result-
ing inA[U+0080][U+009D]B[U+0080][U+009D]C[U+0080][U+009D]D[U+0080][U+009D]. The final image rep-
resents a rotation of the preimage double the acute angle formed by the intersecting reflecting lines.
Chapter 1. Geometry TE - Teaching Tips