1. 7-7 Transformations Warm Up Problem of the Day Lesson Presentation
Course 3

2. 7-7 Transformations Warm Up
Course 3
7-7
Transformations
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.
Course 3
7-7
Transformations
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. Course 3
7-7
Transformations
Learn to transform plane figures using translations, rotations, and reflections.

5. Vocabulary 7-7 Transformations transformation translation rotation
Course 3
7-7
Transformations
Vocabulary
transformation
translation
rotation
center of rotation
reflection
image

6. 7-7 Transformations When you are on an amusement park ride,
Course 3
7-7
Transformations
When you are on an amusement park ride,
you are undergoing a transformation. Ferris wheels and merry-go-rounds are rotations. Free fall rides and water slides are translations. Translations, rotations, and reflections are type of transformations.

7. Course 3
7-7
Transformations
The resulting figure or image, of a translation, rotation or reflection is congruent to the original figure.

8. Additional Example 1: Identifying Transformations
Course 3
7-7
Transformations
Additional Example 1: Identifying Transformations
Identify each as a translation, rotation, reflection, or none of these. A. B.
reflection
rotation
A’ is read “A prime”. The point A is the image of point A.
Reading Math

9. Additional Example 1: Identifying Transformations
Course 3
7-7
Transformations
Additional Example 1: Identifying Transformations
Identify each as a translation, rotation, reflection, or none of these. C. D.
none of the these
translation

10. 7-7 Transformations Check It Out: Example 1
Course 3
7-7
Transformations
Check It Out: Example 1
Identify each as a translation, rotation, reflection, or none of these. A. B. A B A’ B’ C’ A D C A’ B’ C’ D’ C B
translation
reflection

11. 7-7 Transformations Check It Out: Example 1
Course 3
7-7
Transformations
Check It Out: Example 1
Identify each as a translation, rotation, reflection, or none of these. E’ C. D. A’ F’ D’ A B B’ C’ F C D
rotation
none of these E

12. Additional Example 2A: Graphing Transformations
Course 3
7-7
Transformations
Additional Example 2A: Graphing Transformations
Draw the image of the triangle with vertices A(1, 1), B(2, -2), and C(5, 0) after each transformation.
A 180° counterclockwise rotation around (0, 0) y B’ 2 A x C’ C –4 –2 2 4 A’ –2 B

13. Additional Example 2B: Graphing Transformations
Course 3
7-7
Transformations
Additional Example 2B: Graphing Transformations
Draw the image of the triangle with vertices A(1, 1), B(2, -2), and C(5, 0) after each transformation.
A reflection across the y-axis y 2 A’ A x C’ C –4 –2 2 4 –2 B B’

14. 7-7 Transformations Check It Out: Example 2A
Course 3
7-7
Transformations
Check It Out: Example 2A
Draw the image of the triangle with vertices A(1, 2), B(2, –3), and Z(7, 0) after each transformation.
A 180° counterclockwise rotation around (0, 0) y Y’ X 2 x Z’ –4 –2 2 4 Z –2 X’ Y

15. 7-7 Transformations Check It Out: Example 2A
Course 3
7-7
Transformations
Check It Out: Example 2A
Draw the image of the triangle with vertices A(1, 2), B(2, -3), and Z(7, 0) after each transformation.
A reflection across the y-axis y X’ X 2 x Z’ –4 –2 2 4 Z –2 Y’ Y

16. Additional Example 3A: Describing Graphs of Transformations
Course 3
7-7
Transformations
Additional Example 3A: Describing Graphs of Transformations
Rectangle HIJK has vertices H(0, 2), I(4, 2), J(4, 4), and K(0, 4). Find the coordinates of the image of the indicated point after each transformation. y
Translation t units up, point H H’ I’ K’ J’ H I K J H I K J
H’(0, 4) x –2 2

17. Additional Example 3B: Describing Graphs of Transformations
Course 3
7-7
Transformations
Additional Example 3B: Describing Graphs of Transformations
Rectangle HIJK has vertices H(0, 2), I(4, 2), J(4, 4), and K(0, 4). Find the coordinates of the image of the indicated point after each transformation. y
90° rotation around (0, 0), point I H I K J
I’(2, –4) x ‘H ‘K –2 2 ‘I ‘J

18. 7-7 Transformations Check It Out: Example 3A
Course 3
7-7
Transformations
Check It Out: Example 3A
Parallelogram ABCD has vertices A(1, –2), B(3, 2), C(7, 3), and D(6, –1). Find the coordinates of the images of the indicated point after each transformation. y
180° clockwise rotation around (0, 0), point A A B C D B’ A’ C’ D’ 2 x
A’(–1, 2) –2

19. 7-7 Transformations Check It Out: Example 3B
Course 3
7-7
Transformations
Check It Out: Example 3B
Parallelogram ABCD has vertices A(1, –2), B(3, 2), C(7, 3), and D(6, –1). Find the coordinates of the images of the indicated point after each transformation. y
Translation 10 units left, point C A B C D A B C D 2 x
C’(-3, 3) –2

20. 7-7 Transformations Lesson Quiz: Part I
Course 3
7-7
Transformations
Lesson Quiz: Part I
Given the coordinates for the vertices of each pair of quadrilaterals, determine whether each pair represents a translation, rotation, reflection, or none of these.
1. (2, 2), (4, 0), (3, 5), (6, 4)
and
(3, –1), (5, –3), (4, 2), (7, 1)
translation
2. (2, 3), (5, 5), (1, –2), (5, –4)
and
(–2, 3), (–5, 5), (–1, –2), (–5, –4)
reflection

21. 7-7 Transformations Lesson Quiz: Part II
Course 3
7-7
Transformations
Lesson Quiz: Part II
Given the coordinates for the vertices of each pair of quadrilaterals, determine whether each pair represents a translation, rotation, reflection, or none of these.
3. (1, 3), (–1, 2), (2, –3), (4, 0)
and
(1, –3), (–1, 2), (–2, 3), (–4, 0)
none
4. (4, 1), (1, 2), (4, 5), (1, 5)
and
(–4, –1), (–1, –2), (–4, –5), (–1, –5)
rotation