1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Determine if the following sets of points form a parallelogram.
1. (–3, 0), (1, 4), (6, 0), (2, –4)
yes
2. (1, 2), (–2, 2), (–2, 1), (1, –2) no
3. (2, 3), (–3, 1), (1, –4), (6, –2)
yes

3. Move the 9 to the first triangle.
Problem of the Day
How can you move just one number to a different triangle to make the sum of the numbers in each triangle equal? (Hint: There do not have to be exactly 3 numbers in each triangle.)
Move the 9 to the first triangle.

4. Learn to transform plane figures using translations, rotations, and reflections.

5. Vocabulary transformation image translation reflection rotation
center of rotation

6. When you are on an amusement park ride,
you are undergoing a transformation. A transformation is a change in a figure’s position or size.
Translations, rotations, and reflections are types of transformations. The resulting figure, or image, of a translation, rotation, or reflection is congruent to the original figure.
A translation slides a figure along a line without turning.

8. Additional Example 1: Graphing Translations on a Coordinate Plane
Graph the translation of triangle ABC 2 units right and 3 units down.
Add 2 to the x-coordinate of each vertex, and subtract 3 from the y-coordinate of each vertex. A’ B’ C’
Rule
Image
A(–3, 4)A’ (–3 + 2, 4 – 3)
A’(–1, 1)
B(0, 2)B’ (0 + 2, 2 – 3)
B’(2, –1)
C(–2, 1)C’ (–2 + 2, 1 – 3)
C’(0, –2)

9. Check It Out: Example 1
Graph the translation of the quadrilateral ABCD 3 units down and 5 units left.
Subtract 5 from the x-coordinate of each vertex, and subtract 3 from the y-coordinate of each vertex. A’ B’
Rule
Image
A(1, 4)A’ (1 – 5, 4 – 3)
A’(–4, 1)
B(4, 3)B’ (4 – 5, 3 – 3)
B’(–1, 0)
C(4, –1)C’ (4 – 5, –1 – 3)
C’(–1, –4)
C(1, –2)D’ (1 – 5, –2 – 3)
D’(–4, –5) C’ D’ 9

10. A reflection flips a figure across a line to create a mirror image.10

11. 11

12. Additional Example 2: Graphing Reflections on a Coordinate Plane
Graph the reflection of quadrilateral ABCD across the y-axis. B’ A’
Multiply the x-coordinate of each vertex by –1. C’
Rule
Image
A(–4, 1)A’ (–1  –4, 1)
A’(4, 1)
B(–2, 1)B’ (–1  –2, 1)
B’(2, 1)
C(–1, –2)C’ (–1  –1, –2)
C’(1, –2)
D(–4, –3)D’ (–1  –4, –3)
D’(4, –3) D’ 12

13. Graph the reflection of triangle FGH across the x-axis.
Check It Out: Example 2
Graph the reflection of triangle FGH across the x-axis.
Multiply the y-coordinate of each vertex by –1. H’ G’ F’
Rule
Image
F(–4, –2)F’ (–4, –2  –1)
F’(–4, 2)
G(1, –3) G’ (1, –3  –1)
G’(1, 3)
H(–2, –4)H’ (–2, –4  –1)
H’(–2, 4) 13

14. A rotation turns a figure around a point, called the center of rotation.14

15. 15

16. Additional Example 3: Graphing Rotations on a Coordinate Plane
Graph the rotation of triangle ABC 90 counterclockwise about the origin.
Multiply the y-coordinate of each vertex by –1, and switch the x and y coordinates. A’ B’ C’
Rule
Image
A(4, 4)A’ (–1  4, 4 )
A’(–4, 4)
B(4, 1)B’ (–1  1, 4)
B’(–1, 4)
C(2, 1)C’ (–1  1, 2)
C’(–1, 2) 16

17. Graph the rotation of triangle XYZ 180 about the origin.
Check It Out: Example 3
Graph the rotation of triangle XYZ 180 about the origin.
Multiply the both coordinates by –1.
Rule
Image
X(–1, 2)X’ (–1  –1, –1  2 )
X’(1, –2)
Y(2, 3)Y’ (–1  2, –1  3)
Y’(–2, –3)
Z(3, 0)Z’ (–1  3, –1  0)
Z’(–3, 0) Z’ X’ Y’ 17

18. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 18

19. Lesson Quiz
Graph each transformation of triangle ABC.
1. translation 4 units down
2. reflection across the y-axis
3. rotation of 180 about the origin

20. Lesson Quiz for Student Response Systems
1. Give the coordinates of (1, 4) after a translation 3 units up.
A. (4, 4)
B. (4, 7)
C. (–4, –4)
D. (–4, –7) 20

21. Lesson Quiz for Student Response Systems
2. Give the coordinates of (1, 4) after a reflection across the x-axis.
A. (1, 4)
B. (–1, –4)
C. (1, –4)
D. (–1, 4) 21 21

22. Lesson Quiz for Student Response Systems
3. Give the coordinates of (1, 4) after a 90 clockwise rotation around the origin.
A. (4, 1)
B. (4, –1)
C. (1, –4)
D. (–4, 1) 22 22