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Geometry 7-6

Geometry 7-6. Dilations and Similarity in the Coordinate Plane. Learning Targets. Students should be able to… Apply similarity properties in the coordinate plane. Use coordinate proof to prove figures similar. Warm-up. Warm-up Answers. Homework Check. Homework Check. Homework Check.

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Geometry 7-6

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  1. Geometry 7-6 Dilations and Similarity in the Coordinate Plane

  2. Learning Targets • Students should be able to… • Apply similarity properties in the coordinate plane. • Use coordinate proof to prove figures similar.

  3. Warm-up

  4. Warm-up Answers

  5. Homework Check

  6. Homework Check

  7. Homework Check

  8. Homework Check

  9. Dilations and Scale Factors • What is a dilation? • A transformation that changes size but not shape of a figure • What are our tree types of transformations? • Reflections - Flip • Rotations - Turn • Translations - Slide

  10. Dilations and Scale Factors • What is a scale factor? • Describes how much the figure has enlarged or reduced. • How do we use the scale factor? For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by k: (a, b) (ka, kb)

  11. Example 1: Measurement Application • Triangle ABC has vertices A(3, 1), B(0, 1), and C(2, 2). Find the coordinates of the image after a dilation with a scale factor of 2. Graph both the image and pre-image.

  12. Example 1: Measurement Application B. Triangle DEF has vertices A(-2, -2), B(0, 4), and C(6, -2). Find the coordinates of the image after a dilation with a scale factor of . Graph both the image and pre-image.

  13. Example 2: Finding Coordinates of Similar Triangles A. Given that ΔTUO ~ ΔRSO, find the coordinates of U and the scale factor.

  14. Example 2: Finding Coordinates of Similar Triangles B. Given that ΔAOB ~ ΔCOD, find the coordinates of D and the scale factor.

  15. Distance Formula • Who can remember what the distance formula is?

  16. Example 3: Proving Triangles Are Similar A.

  17. Example 4: Using SSS Similarity Theorem A. Graph the image of ΔABC after a dilation B. Graph the image of ΔABC after a dilation with scale factor 2. A(2, 3), B(0, 1), C(3, 0).with scale factor . A(0, 3), B(3, 6), C(6, 0).

  18. Extra Practice

  19. Extra Practice

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