Solutions Section N: Rotations, Reflections, Translations, Symmetry
1. Use a compass and straightedge to find the image of the line under a 180 degree
rotation about the point O.
•Ο
Answer: Choose two arbitrary points P and Q on the line. Use your straightedge to
construct lines PO and QO
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S
P•
•
Ο
•
R
Q •
Use your compass to measure PO and mark off that distance from O on PO to
identify the point R. Similarly, use your compass to measure QO and mark off
that distance from O on QO to identify the point S.
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2. In the diagram below, draw the image of arrow W, reflected across the y-axis and then
rotated 180o about the origin counterclockwise.
The resulting image is shaded red.
3. For each of the following transformations, describe a geometric object that is
transformed to itself by:
(a) reflection
(b) rotation
(c) translation
Solution part a): For example a circle, rectangle, or regular pentagon
Solution part b): For example a circle, rectangle, or regular pentagon
Solution part c): For example a line
4. a) What is the smallest (non zero) angle of rotational symmetry for a regular pentagon?
Answer: 360/5 degrees = 72 degrees
b) How many lines of symmetry does a regular pentagon have? Draw them.
Answer: a regular pentagon has 5 lines of symmetry.