1. Translations, Reflections, and Rotations
Course 2
8-10
Translations, Reflections, and Rotations
Do Now
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)
Hwk: p 77 #1-4

2. EQ: How do I recognize, describe, and show transformations?
GEORGIA PERFORMANCE STANDARDS:
M7G2.a Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to
appropriate transformations;
M7G2.b Given a figure in the coordinate plane, determine the coordinates resulting
from a translation, dilation, rotation, or reflection

3. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
Vocabulary
transformation
image
translation
reflection
line of reflection
rotation

4. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
Vocabulary
Transformation- changes the position or orientation of a figure
Image- resulting figure
Translation- slides without turning
Reflection- flips across a line of reflection
line of reflection- x or y axis
Rotation- turns around a fixed point
Dilation- make bigger or smaller

5. Translations, Reflections, and Rotations
Course 2
8-10
Translations, Reflections, and Rotations
In mathematics, a transformation
changes the position or orientation of a
figure. The resulting figure is the image
of the original. Images resulting from
the transformations described in the next slides are congruent to the original figures.

6. Types of Transformations
Course 2
8-10
Translations, Reflections, and Rotations
Types of Transformations
Translation
The figure slides along a straight line without turning.

7. Types of Transformations
Course 2
8-10
Translations, Reflections, and Rotations
Types of Transformations
Reflection
The figure flips across a line of reflection, creating a mirror image.

8. Types of Transformations
Course 2
8-10
Translations, Reflections, and Rotations
Types of Transformations
Rotation
The figure turns around a fixed point.

9. Additional Example 1: Identifying Types of Transformations
Course 2
8-10
Translations, Reflections, and Rotations
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.

10. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
The point that a figure rotates around may be on the figure or away from the figure.
Helpful Hint

11. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
Check It Out: Example 1
Identify each type of transformation.
A B. x y x y 4 4 2 2 –4 –2 2 4 –4 –2 2 4 –2 –2 –4 –4
The figure slides along a straight line.
The figure turns around a fixed point.
It is a translation.
It is a rotation.

12. Additional Example 2: Graphing Transformations on a Coordinate Plane
Course 2
8-10
Translations, Reflections, and Rotations
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. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
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

14. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
Check It Out: Example 2
Translate quadrilateral ABCD 5 units left and 3 units down. x y B A 4 D’ C’ B’ A’
Each vertex is moved five units left and three units down. 2 C –4 –2 D 2 4 –2 –4

15. Additional Example 3: Graphing Reflections on a Coordinate Plane
Course 2
8-10
Translations, Reflections, and Rotations
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.
x-axis, then y-axis

16. Additional Example 3 Continued
Course 2
8-10
Translations, Reflections, and Rotations
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 ADC are A’(–3, –1), D’(0, 0), C’(2, –2).

17. Additional Example 3 Continued
Course 2
8-10
Translations, Reflections, and Rotations
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 ADC are A’(3, 1), D’(0, 0), C’(–2, 2).

18. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
Check It Out: Example 3A
Graph the reflection of the triangle ABC across the x-axis. Write the coordinates of the vertices of the image. x y
The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites. B 3 C A A’ B’ C’ 3
The coordinates of the vertices of triangle ABC are A’(1, 0), B’(3, –3), C’(5, 0). –3

19. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
Check It Out: Example 3B
Graph the reflection of the triangle ABC across the y-axis. Write the coordinates of the vertices of the image. x y B C 3 –3
The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites. C’ B’ A
The coordinates of the vertices of triangle ABC are A’(0, 0), B’(–2, 3), C’(–2, –3).

20. Additional Example 4: Graphing Rotations on a Coordinate Plane
Course 2
8-10
Translations, Reflections, and Rotations
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 vertex A. 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’

21. Translations, Reflections, and Rotations
Course 2
8-10
Translations, Reflections, and Rotations
Check It Out: Example 4
Triangle ABC has vertices A(0, –2), B(0, 3),
C(0, –3). Rotate ∆ABC 180° about the vertex A. x y B
The corresponding sides, AB and AB’ make a 180° angle. B’ C’ 3 A
Notice that vertex B is 2 units to the right and 3 units above vertex A, and vertex B’ is 2 units to the left and 3 units below vertex A. 3 –3 C

22. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
TOTD
1. Identify the transformation.
reflection
2. The figure formed by (–5, –6), (–1, –6), and
(3, 2) is transformed 6 units right and 2 units
up. What are the coordinates of the new figure?
(1, –4), (5, –4), (9, 4)

23. Insert Lesson Title Here
Course 2
8-10
Translations, Reflections, and Rotations
Insert Lesson Title Here
TOTD
3. Graph the triangle with vertices A(–1, 0), B(–3, 0), C(–1, 4). Rotate ∆ABC 90° counterclockwise around vertex B and reflect the resulting image across the y-axis. x y 2 –2 –4 4 C C’ B’ A’ B A
C’’
A’’
B’’