TRANSFORMATIONS Section 1 7 and 12 1 Geometry

TRANSFORMATIONS Section 1– 7 and 12– 1 Geometry Pre. AP, Revised © 2013 viet. dang@humble. k 12. tx. us 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 1

DEFINITIONS A. A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called a mapping. 1. B. C. Pre–image is the original figure in the transformation (the “before”). Image is the shape that results from the transformation (the “after”). 1. D. E. F. A transformation is an isometry if the size and shape of the figure stay the same. An example include reflections, translations, and rotations. 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. 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 2

TRANSFORMATIONS IN THE COORDINATE PLANE 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 3

TRANSFORMATIONS IN THE COORDINATE PLANE 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 4

GEOGEBRA http: //tube. geogebra. org/material/show/id/13560 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 5

EXAMPLE 1 Identify the transformation. Then use arrow notation to describe the transformation. 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 6

EXAMPLE 2 Identify the transformation. Then use arrow notation to describe the transformation. 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 7

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. 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 8

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. 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 9

REFLECTIONS IN THE COORDINATE PLANE 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 10

EXAMPLE 4 Reflect the figure with the given vertices across the x–axis. X(2, – 1), Y(– 4, – 3), Z(3, 2); x–axis The reflection of (x, y) is (x, –y). Y’ Y 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations X’ Z X Z’ 11

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) 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 12

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. 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations V S U U’ T T’ V’ S’ 13

EXAMPLE 6 Reflect the figure with the given vertices across y = x. S’ R(– 2, 2), S(5, 0), T(3, – 1); y = x The reflection of (x, y) is (–y, x). S R(– 2, 2) R’(2, – 2) S(5, 0) S’(0, 5) T(3, – 1) T’(– 1, 3) 1/16/2022 8: 34 AM R T’ T R’ 1– 7 and 12– 1: Transformations 14

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. 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 15

ASSIGNMENT Worksheet 1/16/2022 8: 34 AM 1– 7 and 12– 1: Transformations 16