Grade 11 Math Worksheet: Dilations

Dilations: Grade 11 Geometry

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. A dilation maps point A(2, 3) to A'(6, 9). What is the scale factor of the dilation?

2. If a dilation has a scale factor of 0.5, what type of transformation is it?

3. The center of dilation is the only point that remains   during a dilation.

4. If the scale factor of a dilation is negative, the image is on the   side of the center of dilation from the preimage.

5. A triangle has vertices at A(1, 1), B(3, 1), and C(1, 4). Dilate the triangle by a scale factor of 2 with the center of dilation at the origin. List the coordinates of the new vertices A', B', and C'.

6. Describe the effect of a dilation with a scale factor of 1 on a geometric figure.

7. Graph the rectangle with vertices D(2, 2), E(4, 2), F(4, 5), and G(2, 5). Then, dilate the rectangle by a scale factor of 0.5 with the center of dilation at the origin. Graph the image D'E'F'G' on the same coordinate plane.

List the coordinates of the dilated vertices:

8. A dilation preserves angle measures.

9. If the scale factor of a dilation is greater than 1, the image is smaller than the preimage.

10. A photograph is 8 inches by 10 inches. You want to enlarge it so that the new dimensions are 12 inches by 15 inches. What is the scale factor of the dilation? Explain your reasoning.