T2 REFLECTIONS
Homework
1. The drawing to the right shows a figure and a
line. Reflect the figure over the line to find its
image.
2. The drawing to the right shows a
figure and its reflected image. Show
how you can move the original to fit
over the image in one reflection by
finding the line of reflection.
3. Find a reflection in real life.
4. Design a reflection of your own.
5. Find the line of reflection if the image of (- 4, 5) is (6, 7)
6. Prove that a reflection is an isometry.
7. Prove that R (l) • R (l) = I.
8. Prove that a reflection is an opposite isometry.
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9. In the figure to the right we are given that
C
the image of C under a reflection in the
line QR is D. Prove that CQ = DQ.
R
Q
D
10. Some capitol letters of the English alphabet have horizontal axis symmetry like C,
while others have vertical axis symmetry like A. List all the letters with horizontal
axis symmetry. List all the letters with vertical axis symmetry.
11. Find a word with horizontal axis symmetry.
12. Find a word with vertical axis symmetry.
13. Draw a triangle and a line m such that R (m) maps the triangle to itself. What kind
of triangle did you use?
14. A person is playing miniature golf at the hole indicated below. The person is
planning a two-wall shot as indicated with a reflection in one wall mapping H to
H’, and a reflection in a second wall mapping H’ to H”. To roll the pall from B to
h, you aim for H”. Show that the total distance traveled by the ball equals the
distance BH”.
H''
H'
H
B
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15. Show how to score a hole in one on the next hole of the golf course shown below
by rolling the ball off one wall.
Ball
2
16. Repeat problem 14 rolling the ball off two walls.
17. Repeat problem 14 rolling the ball off three walls.
18. If a transformation maps two parallel lines to two image lines that are also parallel,
we say that parallelism is invariant under the transformation. Is parallelism
invariant under a reflection?
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