Does the transformation appear to be an isometry? Explain. Translations LESSON 9-1 Additional Examples Does the transformation appear to be an isometry? Explain. The image appears to be the same as the preimage, but turned. Because the figures appear to be congruent, the transformation appears to be an isometry. Quick Check

In the diagram, XYZ is an image of ABC. Translations LESSON 9-1 Additional Examples In the diagram, XYZ is an image of ABC. a. Name the images of B and C. b. List all pairs of corresponding sides. a. Because corresponding vertices of the preimage and the image are listed in the same order, Y is the image of B, and Z is the image of C. b. Because corresponding sides of the preimage and the image are listed in the same order, the following pairs are corresponding sides: AB and XY, AC and XZ, BC and YZ. Quick Check

Find the image of ABC under the translation (x, y)  (x + 3, y – 1). Translations LESSON 9-1 Additional Examples Find the image of ABC under the translation (x, y)  (x + 3, y – 1). Use the rule to find each vertex in the translated image. A(–3, 4) translates to (–3 + 3, 4 – 1), or A'(0, 3). B(–4, –1) translates to (–4 + 3, –1 – 1), or B'(–1, –2). C(–2, 1) translates to (–2 + 3, 1 – 1), or C'(1, 0). The image of ABC is A'B'C' with A'(0, 3), B'(–1, –2), C'(1, 0). Quick Check

Write a rule to describe the translation ABC A B C . Translations LESSON 9-1 Additional Examples Write a rule to describe the translation ABC A B C . Using A(–4, 1) and its image A (2, 0), the horizontal change is 2 – (–4), or 6, and the vertical change is 0 – 1, or –1. You can use any point on ABC and its image on A B C to describe the translation. The translation vector is 6, –1, so the rule is (x, y) (x + 6, y – 1). Quick Check

Tritt’s position after the second delivery is the sum of the vectors. Translations LESSON 9-1 Additional Examples Tritt rides his bicycle 3 blocks north and 5 blocks east of a pharmacy to deliver a prescription. Then he rides 4 blocks south and 8 blocks west to make a second delivery. How many blocks is he now from the pharmacy? The vector 3, 5 represents a ride of 3 blocks north and 5 blocks east. The vector –4, –8 represents a ride of 4 blocks south and 8 blocks west. Tritt’s position after the second delivery is the sum of the vectors. 3, 5 + –4, –8 = 3 + (–4), 5 + (–8) = –1, –3, so Tritt is 1 block south and 3 blocks west of the pharmacy. Quick Check