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Dilations

Dilations. Concept 40. Dilation – the enlarging or reducing of an objects size according to a specific scale factor k around a center of dilation. If a point of the image is the center of dilation, then it stays the same.

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Dilations

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  1. Dilations Concept 40

  2. Dilation – the enlarging or reducing of an objects size according to a specific scale factor k around a center of dilation. • If a point of the image is the center of dilation, then it stays the same. • If a point is not on the center of dilation, then it is moved along a ray joining the center of dilation and the point. It is found by multiplying the pre-image length times the scale factor.

  3. A P A P Plot the image of point A under each described dilation around point P. 1. scale factor of 3 2. Scale factor of ½

  4. A dilation was performed on each shape. Identify the scale factor and the point of dilation. 3. 4. 12 4

  5. Each image is the result of a dilation of the preimage. Identify the correct center of dilation. 5. 6. Point C Point D 7. 8. Point A Point D

  6. P Each image is the dilation of an image with point P as the point of dilation. Perform each dilation and answer each question. P 9. Dilation with a scale factor of 2. What is the length of A'B'? 10. Dilation with a scale factor of 3/2. What is the length C'D'? A’ A’ C’ B’ B’ C’ D’

  7. Perform each dilation. 11. ABC with A(-3, 1), B(0, 2) and C(-2, -3) with a center of point C and scale factor of 2. 12. ABC with A(-5, -4), B(7, -7) and C(-2, 2) with a center of point P(1, -4) and scale factor of 1/3. B’ P A’ C’ A’ B’ C’

  8. 13. ABC with A(3, -6), B(1, -6) and C(2, -4) with a center of point P(2, -6) and scale factor of 4. 14. ABC with A(-6, 2), B(6, 6) and C(2, -6) with a center of point A and scale factor of ¼ . B’ A’ A’ C’ P B’ C’ A C B

  9. 15. ∆A’B’C is the result of dilating ∆ABC about point C by a scale factor of 2. Perform the dilation and then select all correct statements that are true. • BC and B'C' have the same lengths. • AB and A'B' are on parallel lines. • The measures of ∠C and ∠C' are equal D. None of the above C’ B’ A’

  10. 16. Quadrilateral A’B’C’D’ is the result of dilating quadrilateral ABCD about point P by a scale factor of 2/3. Select all correct statements that are true. • The measures of ∠A and ∠A' are equal. • AB and A'B' are parallel lines. C. Points D and D’ have the same coordinates. D. None of the above

  11. 17. Quadrilateral A’B’C’D’ is the result of dilating quadrilateral ABCD about point P by a scale factor of 3/2. Select all correct statements that are true. • BC and B'C' are on parallel lines. B. The measures of ∠D and ∠D' are equal. C. AD and A'D' are on the same line. D. None of the above A’ D’ C’ B’

  12. 18. ∆A’B’C is the result of dilating ∆ABC about point C by a scale factor of 3. Select all correct statements that are true. • The measures of ∠A and ∠A' are equal. B. BC and B'C' are on the same line. C. ∆ABC and ∆A'B'C' have the same perimeters. D. None of the above.

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