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

2. Warm Up
1. Subtract 3 from the x-coordinate and 2 from the y-coordinate in (7, –4).
(4, –6)‏
2. Multiply each coordinate by 3 in (4, 9).
(12, 27)‏
3. Subtract 4 from the x-coordinate and add 3 to the to the y-coordinate in (–2, –1).
(–6, 2)‏

3. Problem of the Day
Some numbers appear as different numbers when rotated or reflected. Name as many as you can.
Possible answers: 6 and 9; and 6669; IV and VI; IX and XI

4. Sunshine State Standards
MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane.
Also MA.7.G.4.3

5. Vocabulary transformation image preimage translation reflection
line of reflection
rotation

6. In mathematics, a transformation
changes the position or orientation of a
figure. The resulting figure is the image
of the original figure, called the preimage. Images resulting from the transformations described in the next slides are congruent to the original figures.

7. Types of Transformations
Translation
The figure slides along a straight line without turning.

8. Types of Transformations
Reflection
The figure flips across a line of reflection, creating a mirror image.

9. Types of Transformations
Rotation
The figure turns around a fixed point.

10. Additional Example 1: Identifying Types of Transformations
Identify each type of transformation. A. B.
The figure flips across the y-axis.
The figure slides along a straight line.
It is a reflection.
It is a translation.

11. Check It Out: Example 1
Identify the type of transformation.
translation

12. Additional Example 2: Graphing Transformations on a Coordinate Plane
Graph the translation of quadrilateral ABCD 4 units left and 2 units down.
Each vertex is moved 4 units left and 2 units down.

13. Additional Example 2 Continued
Write the coordinate of the vertices of the image.
Quadrilateral ABCD
(x – 4, y – 2)
A’B’C’D’
A(1, 3)
(1 – 4, 3 – 2)
A’(–3, 1)
B(4, 4)
(4 – 4, 4 – 2)
B’(0, 2)
C(4, 1)
(4 – 4, 1 – 2)
C’(0, –1)
D(1, –1)
(1 – 4, –1 – 2)
D’(–3, –3)
The coordinates of the vertices of quadrilateral A'B'C'D'
are A'(–3, 1), B'(0, 2), C'(0, –1), and D'(–3, –3).

14. Reading Math
A’ is read “A prime” and is used to represent the point on the image that corresponds to point A of the original figure

15. Check It Out: Example 2
Graph the translation of quadrilateral ABCD 5 units left and 3 units down. x y A B C 2 –2 –4 4 D D’ C’ B’ A’

16. Additional Example 3: Graphing Reflections on a Coordinate Plane
Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image.

17. Additional Example 3 Continued
A. x-axis
The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites.
The coordinates of the vertices of triangle A’D’C’ are A’(–3, –1), D’(0, 0), and C’(2, –2).

18. Additional Example 3 Continued
B. y-axis
The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites.
The coordinates of the vertices of triangle A’D’C’ are A’(3, 1), D’(0, 0), and C’(–2, 2).

19. Check It Out: Example 3
Graph the reflection of quadrilateral ABCD across the x-axis.

20. Additional Example 4: Graphing Rotations on a Coordinate Plane
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° about the origin. Write the coordinates of the vertices of the image. x y A B C 3 –3
The corresponding sides, AC and AC’ make a 180° angle.
Notice that vertex C is 4 units to the right of vertex A, and vertex C’ is 4 units to the left of vertex A. C’ B’ A’
The coordinates of the vertices of triangle A’B’C’ are A’(0, 0), B’(–2, –3), and C’(–4, 0).

21. Check It Out: Example 4
Rotate the graph of quadrilateral ABCD 90° clockwise about the origin.

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

23. Lesson Quiz
1. Identify the transformation.
reflection
2. The figure formed by (–5, –6), (–1, –6), and
(3, 2) is translated 6 units right and 2 units up. What are the coordinates of the new figure?
(1, –4), (5, –4), (9, 4)‏
3. Graph the triangle with vertices A(0, 0), B(–3, 0), C(–1, 4). Reflect ∆ABC across the y-axis and give the coordinates of the vertices of the image.
A'(0, 0), B'(3, 0), C'(1, 4)‏

24. Lesson Quiz for Student Response Systems
1. Identify the transformation.
A. translation
B. reflection
C. rotation
D. none

25. Lesson Quiz for Student Response Systems
2. The figure formed by (–3, 2), (–4, 1), and (–1, –5) is translated 3 units right and 5 units up. What are the coordinates of the new figure?
A. (–6, –3), (–7, –4), (–4, –10)
B. (0, 7), (–7, –4), (2, –10)
C. (0, 7), (–1, 6), (2, 0)
D. (–6, –3), (–1, 6), (–4, 0)