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Learn about translations in the coordinate plane with examples, practice exercises, and real-world applications.

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Splash Screen

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 9–1) CCSS Then/Now New Vocabulary Key Concept: Translation Example 1: Draw a Translation Key Concept: Translation in the Coordinate Plane Example 2: Translations in the Coordinate Plane Example 3: Real-World Example: Describing Translations Lesson Menu

  3. Name the reflected image of BC in line m. ___ A. B. C. D. 5-Minute Check 1

  4. Name the reflected image of AB in line m. ___ A. B. C. D. 5-Minute Check 2

  5. Name the reflected image of ΔAGB in line m. A.ΔFGE B.ΔEGD C.ΔCGD D.ΔBCG 5-Minute Check 3

  6. Name the reflected image of B in line m. A.D B.E C.F D.G 5-Minute Check 4

  7. Name the reflected image of ABCF in line m. A.AFEB B.DCBE C.EDCF D.FEDA 5-Minute Check 5

  8. A.B. C.D. Which of the following shows a reflection in the x-axis? 5-Minute Check 6

  9. Content Standards G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Mathematical Practices 5 Use appropriate tools strategically. 4 Model with mathematics CCSS

  10. You found the magnitude and direction of vectors. • Draw translations. • Draw translations in the coordinate plane. Then/Now

  11. translation vector Vocabulary

  12. Concept

  13. Step 1 Draw a line through each vertex parallel to vector . Step 2 Measure the length of vector . Locate point G'by marking off this distance along the line through vertex G, starting at G and in the same direction as the vector. Draw a Translation Copy the figure and given translation vector. Then draw the translation of the figure along the translation vector. Example 1

  14. Draw a Translation Step 3 Repeat Step 2 to locate points H', I', and J' to form the translated image. Answer: Example 1

  15. A.B. C.D. Which of the following shows the translation of ΔABC along the translation vector? Example 1

  16. Concept

  17. Translations in the Coordinate Plane A. Graph ΔTUV with vertices T(–1, –4), U(6, 2), and V(5, –5) along the vector –3, 2. Example 2

  18. Translations in the Coordinate Plane The vector indicates a translation 3 units left and 2 units up. (x, y)→ (x – 3, y + 2) T(–1, –4)→ (–4, –2) U(6, 2)→ (3, 4) V(5, –5)→ (2, –3) Answer: Example 2

  19. Translations in the Coordinate Plane B. Graph pentagon PENTA with vertices P(1, 0), E(2, 2), N(4, 1), T(4, –1), and A(2, –2) along the vector –5, –1. Example 2

  20. Translations in the Coordinate Plane The vector indicates a translation 5 units left and 1 unit down. (x, y)→ (x – 5, y – 1) P(1, 0)→ (–4, –1) E(2, 2)→ (–3, 1) N(4, 1)→ (–1, 0) T(4, –1)→ (–1, –2) A(2, –2)→ (–3, –3) Answer: Example 2

  21. A. Graph ΔABC with the vertices A(–3, –2), B(4, 4), C(3, –3) along the vector –1, 3. Choose the correct coordinates for ΔA'B'C'. A.A'(–2, –5), B'(5, 1), C'(4, –6) B.A'(–4, –2), B'(3, 4), C'(2, –3) C.A'(3, 1), B'(–4, 7), C'(1, 0) D.A'(–4, 1), B'(3, 7), C'(2, 0) Example 2

  22. B. Graph ΔGHJK with the vertices G(–4, –2), H(–4, 3), J(1, 3), K(1, –2) along the vector 2, –2. Choose the correct coordinates for ΔG'H'J'K'. A.G'(–6, –4), H'(–6, 1), J'(1, 1), K'(1, –4) B.G'(–2, –4), H'(–2, 1), J'(3, 1), K'(3, –4) C.G'(–2, 0), H'(–2, 5), J'(3, 5), K'(3, 0) D.G'(–8, 4), H'(–8, –6), J'(2, –6), K'(2, 4) Example 2

  23. Describing Translations A. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 2 to position 3 in function notation and in words. Example 3

  24. Describing Translations The raindrop in position 2 is (1, 2). In position 3, this point moves to (–1, –1). Use the translation function (x, y) → (x + a, y + b) to write and solve equations to find a and b. (1 + a, 2 + b) or (–1, –1) 1 + a = –1 2 + b = –1 a = –2 b = –3 Answer: function notation: (x, y) → (x – 2, y – 3) So, the raindrop is translated 2 units left and 3 units down from position 2 to 3. Example 3

  25. Answer: translation vector: Describing Translations B. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 3 to position 4 using a translation vector. (–1 + a, –1 + b) or (–1, –4) –1 + a = –1 –1 + b = –4 a = 0 b = –3 Example 3

  26. A. The graph shows repeated translations that result in the animation of the soccer ball. Choose the correct translation of the soccer ball from position 2 to position 3 in function notation. A. (x, y) → (x + 3, y + 2) B. (x, y) → (x + (–3), y + (–2)) C. (x, y) → (x + (–3), y + 2) D. (x, y) → (x + 3, y + (–2)) Example 3

  27. B. The graph shows repeated translations that result in the animation of the soccer ball. Describe the translation of the soccer ball from position 3 to position 4 using a translation vector. A.–2, –2 B.–2, 2 C.2, –2 D.2, 2 Example 3

  28. End of the Lesson

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