1. Geometry PreAP, Revised ©2013 1–7 and 12–1: Transformations
Section 1–7 and 12–1
Geometry PreAP, Revised ©2013
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1–7 and 12–1: Transformations

2. 1–7 and 12–1: Transformations
Definitions
A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called a mapping.
A transformation is an isometry if the size and shape of the figure stay the same. An example include reflections, translations, and rotations.
Pre–image is the original figure in the transformation (the “before”).
Image is the shape that results from the transformation (the “after”).
Since it comes from transforming the original figure, it is labeled with the same letters but with a′ (prime) symbol after each letter. For example, after a reflection, ΔABC becomes ΔA′B′C′.
A reflection is a transformation across a line so that the line of reflection is the perpendicular bisector of the segment joining each point and its image.
Rotation is also known as a turn where each point and its image are the same distance from the center of rotation
Translation is also known as a slide where all of the points of the figure move in the same distance.
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1–7 and 12–1: Transformations

3. Transformations in the Coordinate Plane
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1–7 and 12–1: Transformations

4. Transformations in the Coordinate Plane
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1–7 and 12–1: Transformations

5. 1–7 and 12–1: Transformations
Geogebra
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1–7 and 12–1: Transformations

6. 1–7 and 12–1: Transformations
Example 1
Identify the transformation. Then use arrow notation to describe the transformation.
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1–7 and 12–1: Transformations

7. 1–7 and 12–1: Transformations
Example 2
Identify the transformation. Then use arrow notation to describe the transformation.
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1–7 and 12–1: Transformations

8. 1–7 and 12–1: Transformations
Example 3
A figure has vertices at E(2, 0), F(2, –1), G(5, –1), and H(5, 0). After a transformation, the image of the figure has vertices at E’(0, 2), F’(1, 2), G’(1, 5), and H’(0, 5). Draw the preimage and image. Then, identify the transformation.
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1–7 and 12–1: Transformations

9. 1–7 and 12–1: Transformations
Your Turn
A figure has vertices at X(–1, 1), Y(1, 4), and Z(2, 2). After a transformation, the image of the figure has vertices at X'(–3, 2), Y'(–1, 5), and Z'(0, 3). Draw the preimage and the image. Identify the transformation.
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1–7 and 12–1: Transformations

10. Reflections in the Coordinate Plane
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1–7 and 12–1: Transformations

11. 1–7 and 12–1: Transformations
Example 4
Reflect the figure with the given vertices across the x–axis.
X(2, –1), Y(–4, –3), Z(3, 2); x–axis Y’
The reflection of (x, y) is (x,–y). Z X’ X Z’ Y
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1–7 and 12–1: Transformations

12. 1–7 and 12–1: Transformations
Example 5
Reflect the points of with the given vertices across the y–axis given the points of F(–4, 2), G(–3, –1) and H(3, 3)
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1–7 and 12–1: Transformations

13. 1–7 and 12–1: Transformations
Your Turn
Reflect the rectangle with vertices S(3, 4), T(3, 1), U(–2, 1) and V(–2, 4) across the x–axis. Then, identify the new points. V S U T V’ S’ U’ T’
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1–7 and 12–1: Transformations

14. 1–7 and 12–1: Transformations
Example 6
Reflect the figure with the given vertices across y = x. S’ R’ T’
R(–2, 2), S(5, 0), T(3, –1); y = x S R T
The reflection of (x, y) is (–y, x).
R(–2, 2) R’(2, –2)
S(5, 0) S’(0, 5)
T(3, –1) T’(–1, 3)
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1–7 and 12–1: Transformations

15. 1–7 and 12–1: Transformations
Your Turn
Reflect the rectangle with vertices A(3, 4), B(3, 1), and C(–2, 1) across the line of y = x. Then, identify the new points.
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1–7 and 12–1: Transformations

16. 1–7 and 12–1: Transformations
Assignment
Worksheet
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1–7 and 12–1: Transformations