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Translations

4.  C ?. 6.  B ?. 2. EG ?. Translations. Lesson 9-1. Check Skills You’ll Need. (For help, go to Lesson 4-1.). ABC EFG . Complete the congruence statements. 1. AB ? 3. FG ? 5. E ? 7. Complete: If KTQ LGR , then TK ? and TQK ?.

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Translations

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  1. 4. C? 6. B? 2.EG ? Translations Lesson 9-1 Check Skills You’ll Need (For help, go to Lesson 4-1.) ABCEFG. Complete the congruence statements. 1.AB? 3.FG? 5. E? 7. Complete: If KTQLGR, then TK? and TQK? . Check Skills You’ll Need 9-1

  2. Translations Lesson 9-1 Check Skills You’ll Need Solutions 1. Choose letters from the same positions in the congruence statement ABCEFG: AB EF 2. Choose letters from the same positions in the congruence statement ABCEFG: EGAC 3. Choose letters from the same positions in the congruence statement ABC EFG: FG BC 4. Choose the letter in the same position of the congruence statement ABC EFG: C G 5. Choose the letter in the same position of the congruence statement ABC EFG: E A 6. Choose the letter in the same position of the congruence statement ABC EFG: B F 7. Choose the letter(s) in the same position of the congruence statement KTQ LGR: TK GL and TQK GRL 9-1

  3. Warm-up

  4. Translations Lesson 9-1 A transformation of a geometric figure is a change in its position, shape, or size. The original figure is the preimage. The resulting figure is an image. An isometry is a transformation in which the preimage and image are congruent. Translations (slides), reflections (flips), and rotations (turns) are isometries. 9-1

  5. Translations Lesson 9-1 A transformation maps a figure onto its image and may be described with arrow (→) notation. Prime (´) notation is sometimes used to identify image points. 9-1

  6. Translations Lesson 9-1 In the diagram at the right, K’ is the image of K (K→K’). Read K→K’ as “K maps onto K prime.” Notice that you list corresponding points of the preimage and image in the same order, as you do for corresponding points of congruent or similar figures. 9-1

  7. Translations Lesson 9-1 A translation (or slide) is an isometry that maps all points of a figure the same distance in the same direction. 9-1

  8. Translations Lesson 9-1 A composition of transformations is a combination of two or more transformations. In a composition, each transformation is performed on the image of the preceding transformation. In general, the composition of any two translations is a translation. 9-1

  9. Translations Lesson 9-1 Additional Examples Identifying Isometries 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 9-1

  10. a. Name the images ofB and 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. 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. Translations Lesson 9-1 Additional Examples Naming Images and Corresponding Parts In the diagram, XYZ is an image of ABC. b. List all pairs of corresponding sides. Quick Check 9-1

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

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

  13. Translations Lesson 9-1 Additional Examples Real-World Connection 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  5, 3  represents a ride of 3 blocks north and 5 blocks east. The vector  –8, –4  represents a ride of 4 blocks south and 8 blocks west. Tritt’s position after the second delivery is the sum of the vectors.  5, 3  +  –8, –4  =  5 + (–8), 3 + (–4)  =  –3, –1 , so Tritt is 1 block south and 3 blocks west of the pharmacy. Quick Check 9-1

  14. AB and DA B and D Translations Lesson 9-1 Lesson Quiz 1. Is the transformation below an isometry? Explain. No; the angles are not congruent. For Exercises 2 and 3, ABCD is an image of KLMN. 2. Name the images of L and N. 3. Name the sides that correspond to KL and NK. Use the diagram below. 4. Find the image of MNV under the translation (x, y)  (x – 2, y + 5). M(–5, 4), N(–4, 6), V(–1, 5) 5. Write a rule to describe the translation MNV WZP. (x, y)  (x + 4, y + 3) 9-1

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