9-6 Study Guide and Intervention Dilations Draw Dilations A dilation is a similarity transformation that enlarges or reduces a figure proportionally. Dilations are completed with respect to a center and a scale factor. Example: Draw the dilation image of with center and = 2. O r Draw and Label points and so that = 2(OA), , , . A′, B′, C′ OA′ = 2(OB) and = 2(OC). connect the points to draw OB′ OC′ △A′B′C′. is a dilation of △A′B′C′ △ABC. Exercises Use a ruler to draw the image of the figure under a dilation with center and the scale factor indicated. S r 1. = 2 2. = r r 3. = 1 4. = 3 r r 5. = 6. = 1 r r 9-6 Study Guide and Intervention (continued) Dilations Dilations In The Coordinate Plane To find the coordinates of an image after a dilation centered at the origin, multiply the and of each point on the preimage by the scale factor of the dilation, x- y-coordinates r. (x, (rx, y) ry) → Example: has vertices and 0). Find the image of after a dilation centered at A(–2, B(1, C(2, –2), –1), the origin with a scale factor of 2.
9-6 Study Guide and Intervention Dilations Draw Dilations A dilation is a similarity transformation that enlarges or reduces a figure proportionally. Dilations are completed with respect to a center and a scale factor. Example: Draw the dilation image of with center O and r = 2. Draw , , and . Label points A′, B′, and C′ so that OA′ = 2(OA), OB′ = 2(OB) and OC′ = 2(OC). connect the points to draw △A′B′C′. △A′B′C′ is a dilation of △ABC. Exercises Use a ruler to draw the image of the figure under a dilation with center S and the scale factor r indicated. 1. r = 2 2. r = 3. r = 1 4. r = 3 5. r = 6. r = 1 9-6 Study Guide and Intervention (continued) Dilations Dilations In The Coordinate Plane To find the coordinates of an image after a dilation centered at the origin, multiply the x- and y-coordinates of each point on the preimage by the scale factor of the dilation, r. (x, y) → (rx, ry) Example: has vertices A(–2, –2), B(1, –1), and C(2, 0). Find the image of after a dilation centered at the origin with a scale factor of 2.