1. Translations
Lesson 9-8

2. Translations Translations are used on the coordinate plane.
A translation is a shift or movement of a figure a given number of places on the coordinate plane.

3. EXAMPLE Suppose we have parallelogram ABCD as shown on the graph.
We can “translate” this shape
5 units to the right and 3 units
down. The new image would
look like this: A B C D

4. Notice that the entire new image
Is shifted 5 units to the right and
3 units down. The labels of the
image are noted with a prime ‘
symbol. A B A’ B’ C D C’ D’

5. TRY THIS Translate triangle QRS 4 units to The left and 5 units up. Q

6. TRY THIS Q’ Translate triangle QRS 4 units to The left and 5 units up.

7. Symmetry and Reflections
Lesson 9-9

8. Reflection is a mirror image of a figure.
In geometry, reflectional symmetry occurs when one half of a figure is a mirror image of the other half.
The line of symmetry is the line that divides a figure into two congruent halves.

9. Symmetry
Notice that one half of the pentagon is the mirror image of the other.
Line of symmetry

10. Try This
Which of the following figures have reflectional symmetry?

11. Try This Which of the following figures have reflectional symmetry?
YES NO
YES
YES
YES

12. Symmetry
Many figures have more than one line of symmetry. Notice that the square has 4 lines of symmetry.

13. Try This
Draw all the lines of symmetry for the following figures.

14. Try This
Draw all the lines of symmetry for the following figures.

15. Try This
Draw all the lines of symmetry for the following figures.

16. Try This
Draw all the lines of symmetry for the following figures.

17. Try This
Draw all the lines of symmetry for the following figures.

18. Try This
Draw all the lines of symmetry for the following figures.

19. Reflections Reflections can also be used on the coordinate plane.
A reflection is a figure that has been flipped over a line of reflection.

20. EXAMPLE
Suppose that line segment AB is graphed as shown. If it is reflected over the y-axis, it would look like this: A B

21. EXAMPLE Notice that the image of the line
segment is a mirror image of the
original one. It is as if the paper
were folded on the y-axis and it left an identical imprint on the other side of the axis. A A’ B B’

22. Try This Graph the image of triangle DEF
after a reflection over the x-axis. D E F

23. Try This D E F F’ E’ D’

24. Try This Now graph the image of parallelogram ABCD after it is
reflected over x = 2 A B C D

25. Try This Line of reflection A B B’ A’ C D D’ C’
Notice that the line of
reflection is x = 2. It is as
if the paper were folded on
the line x = 2.