1. To draw a dilation of quadrilateral ABCD with E as the center and sides 1/2 as long, connect each vertex (A, B, C, D) to point E with a straight line. On each of these lines, locate a new point (A', B', C', D') such that the distance from E to the new point is exactly half the distance from E to the original vertex. Connect A', B', C', and D' to form the dilated image.
2. The scale factor of the dilation shown is 1/2. This is determined by comparing corresponding side lengths or distances from the center of dilation; for example, if a side of the smaller figure measures 2 units and the corresponding side of the larger figure measures 4 units, the ratio is 2/4 = 1/2.
3. For D₀.₇₅(△ABC), given A(4, -3), B(6, 1), C(10, -1):
- A'(3, -2.25)
- B'(4.5, 0.75)
- C'(7.5, -0.75)
4. For D₁.₅(△XYZ), given X(3, 0), Y(4, 2), Z(6, -2):
- X'(4.5, 0)
- Y'(6, 3)
- Z'(9, -3)
5. D₄(△ABC) has a perimeter of 100 units and an area of 625 units².
a. The perimeter of △ABC is 25 units. (Perimeter scales linearly: 100 / 4 = 25)
b. The area of △ABC is 39.0625 units². (Area scales by the square of the scale factor: 625 / 4² = 625 / 16 = 39.0625)
6. Charles enlarged the small kite MNOP to make a design for an art project.
a. The side lengths of the image are twice as long as the side lengths of the preimage.
b. The area of the image is four times the area of the preimage.
c. The scale factor of the dilation Charles used to enlarge the kite is 2.
Parent Tip: Review the logic above to help your child master the concept of dilations practice worksheet answers.
