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Transformations: Dilation

Transformations: Dilation. Unit 4.04. Vocabulary. Dilation: A transformation in which a figure is made larger or smaller with respect to a point called the center of dilation. Example: The red polygon has been Dilated (made larger) to form the blue polygon. Vocabulary.

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Transformations: Dilation

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  1. Transformations: Dilation Unit 4.04

  2. Vocabulary • Dilation: A transformation in which a figure is made larger or smaller with respect to a point called the center of dilation. • Example: The red polygon has been Dilated (made larger) to form the blue polygon.

  3. Vocabulary • Center of Dilation: The point from which a figure is dilated. When graphed on the Cartesian Plane, the Origin is often the Center of Dilation. • Example: Here, the Origin (0, 0) is the Center of Dilation. Center of Dilation (0, 0)

  4. Vocabulary • Scale Factor: In a dilation, the original figure and dilated image are similar. The ratio that compares the one with the other is called the Scale Factor and is called k. • Example: The blue square is twice the size of the redsquare. If red blue, then what is the scale factor? k = 2 k = ½ What if blue red?

  5. Vocabulary • Dilation on the Cartesian Plane: To dilate a figure in respect to the origin, multiply the coordinates of each vertex by the scale factor, k.

  6. Vocabulary • Dilation on the Cartesian Plane: To dilate a figure in respect to the origin, multiply the coordinates of each vertex by the scale factor, k. • Transformation Notation of Dilations: (x, y)  (kx, ky) • Classifying a Dilation by the Scale Factor: • When k > 1, the dilation is an enlargement • When 0 < k < 1, the dilation is a reduction

  7. Vocabulary • Example 1: Dilate ΔABC by the scale factor, k = 3, then classify it.

  8. Vocabulary • Example 2: Dilate Rectangle WXYZ by the scale factor, k = ½ (or 0.5), then classify it.

  9. You Try It!

  10. 1) Dilate ΔABC by a scale factor, k = 2, then classify it. (1,3) A: _____________ B: _____________ C: ____________ A’: ____________ B’: ____________ C’: ____________ (4,0) A’ A (-3,-2) B (2,6) B’ C C’ (8,0) (-6,-4)

  11. Dilate ΔXYZ by a scale factor, k = 1/3, then classify it. 2) (3,9) X: _____________ Y: _____________ Z: _____________ X’: ____________ Y’: ____________ Z’: ____________ X (9,0) X’ (-3,-3) Y Y’ (1,3) Z’ Z (3,0) (-1,-1)

  12. 3) Dilate ΔJKL by a scale factor, k= 2. Then translate it down 5 and to the right 5 units. (2,1) (-5,3) (-1,-2) J: ____________ K: ____________ L: ____________ (-2,-4) J’: ____________ K’: ____________ L’: ____________ J’’: ___________ K’’: ___________ L’’: ____________ L’ (4,2) (-10,6) L K’ K L’’ (3,-9) K’’ J (9,-3) J’ (-5,1) J’’

  13. Homework Time  Scale It! -- Dilations WS

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