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Understanding Figures and Vectors: Transformations in Geometry

Explore transformations, translations, and isometries to manipulate and understand figures in geometry effectively. Learn how to apply translation rules and discover the preimage and images of transformed figures using vector moves.

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Understanding Figures and Vectors: Transformations in Geometry

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  1. Unit 2 Translate Figures and Use Vectors

  2. Moves or changes a figure Transformation: Original figure Preimage: Image: Transformed figure “P prime” A congruent transformation Isometry:

  3. Translation: An isometry that moves every point a certain distance in a certain direction P Q

  4. Translation: Note: and

  5. Motion Rule: Moves each point left, right, down, or up Down or Up Left or Right

  6. Use the translation What is the image of D(4, 7)? (4 + 2, 7 – 5) D +2 (6, 2) –5

  7. Use the translation What is the image of R(2, –4)? (2 – 7, –4 + 4) (–5, 0) +4 –7 R

  8. Use the translation What is the preimage of (–5, 3)? M (–5 – 4, 3 + 6) (–9, 9) +6 –4

  9. Use the translation What is the preimage of (4, –1)? (4 + 5, –1) (9, –1) +5 A

  10. The vertices of ABC are A(–1, 1), B(4, –1), and C(2, 4). Graph the image of the triangle using prime notation. (–1 – 3, 1 + 5) (–4, 6) C (4 – 3, –1 + 5) A (1, 4) B (2 – 3, 4 + 5) (–1, 9)

  11. The vertices of ABC are A(–1, 1), B(4, –1), and C(2, 4). Graph the image of the triangle using prime notation. (–1 , 1 – 3) (–1, –2) C (4, –1 – 3) A (4, –4) B (2, 4 – 3) (2, 1)

  12.  is the image of ABC after a translation. Write a rule for the translation. +3 –5

  13.  is the image of ABC after a translation. Write a rule for the translation. +2 –5

  14. Find the value of each variable in the translation. a = 80° 2b = 8 b = 4 c = 13 5d = 100 d = 20°

  15. Find the value of each variable in the translation. b – 5 = 12 b = 17 3c + 2 = 20 3c = 18 c = 6 a = 180 – 90 – 31 a = 59°

  16. HW Problems

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