Grade 12 Math: Dilations Worksheet
This worksheet focuses on dilations in geometry, covering definitions, properties, and applying dilation transformations to figures on a coordinate plane.
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Grade 12 Math: Dilations
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following statements is true about a dilation?
It changes the size of a figure but not its shape.
It changes the shape of a figure but not its size.
It changes both the size and shape of a figure.
It is a rigid transformation.
2. If a point (x, y) is dilated by a scale factor of k with the origin as the center of dilation, what are the coordinates of the image?
(x + k, y + k)
(x - k, y - k)
(kx, ky)
(x/k, y/k)
3. A dilation with a scale factor greater than 1 results in an of the original figure.
4. A dilation with a scale factor between 0 and 1 results in a of the original figure.
5. The of dilation is the fixed point about which a figure is enlarged or reduced.
6. Triangle ABC has vertices A(1, 2), B(3, 1), and C(2, 4). Dilate triangle ABC by a scale factor of 2 with the center of dilation at the origin. List the coordinates of the image A'B'C'.
7. Describe the effect of a dilation with a negative scale factor.
8. Graph the quadrilateral with vertices D(-4, 4), E(4, 4), F(4, -4), and G(-4, -4). Then, dilate the quadrilateral by a scale factor of 0.5 with the center of dilation at the origin, and graph the image D'E'F'G'.
9. A dilation preserves angle measures.
True
False
10. The ratio of the perimeter of the image to the perimeter of the pre-image after a dilation is equal to the square of the scale factor.
True
False
11. A rectangle has vertices at P(0,0), Q(6,0), R(6,3), and S(0,3). If the rectangle is dilated with a center of dilation at (2,1) and a scale factor of 3, find the coordinates of the image P'Q'R'S'. Show your work.