8.2.7 Dilations.

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Presentation transcript:

8.2.7 Dilations

TIP: All dilations are similar figures Vocabulary TIP: All dilations are similar figures Dilation – A transformation in which an object is made bigger or smaller from the same point Center of Dilation – The point from which an object dilates

Identifying a Dilation

Your Turn!

Scale Factor Scale Factor – The side length ratio of two similar figures To dilate a figure in the coordinate plane, using the origin as the center of dilation, multiply the coordinates of each original vertex by the scale factor.

Scale Factor Example: if a triangle’s coordinates are (0, 2) (2, 2) (2,0) and the scale factor for its dilation is 3, then the new coordinates would be (0, 6) (6, 6) (6, 0) Note: When the scale factor is greater than 1, the dilation is an enlargement. When the scale factor is less than 1, the dilation is a reduction. These are called TYPES of dilations: enlargement or reduction

Scale Factor Example (0, 2) (2, 2) (2,0) x3 (0, 6) (6, 6) (6, 0)

Dilating a Figure Vertices of ABC (3x, 3y) Vertices of A’B’C’ A (1, 3) Draw the image of Triangle ABC after a dilation with a scale factor of 3. Identify the type of dilation. Vertices of ABC (3x, 3y) Vertices of A’B’C’ A (1, 3) (3 ∙ 1, 3 ∙ 3) A’ (3, 9) B (2, 3) (3 ∙ 2, 3 ∙ 3) B’ (6, 9) C (2, 1) (3 ∙ 2, 3 ∙ 1) C’ (6, 3)

Homework Page 87 (#5, 6, 9, 12, 17, 18, 19, 21, 25, 33)