Question

Determine whether one figure is a dilation of the other. Complete the justification.

Quadrilateral DEFG has side lengths of 16 m, 32 m, 28 m, and 12 m. Quadrilateral D'E'F'G' has side lengths of 44 m, 88 m, 77 m, and 33 m.

The figure D' E' F' G' (is/is not) a dilation of the figure D E F G. Thr ratios of the lengths of the corresponding sides (are not/are) equal.​

Answer 1

is a dilation

Explanation:

One of the triangles will be a dilation of the other if corresponding sides have the same ratio. When given a series of side lengths, there are a couple of ways you can determine if the ratios are the same.

• compute the ratio of the side of one figure to the corresponding side of the other figure
• put corresponding side lengths in order around the figure, and remove any common factor from their values.

Sometimes the latter approach is easier.

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DEFG ratios are 16 : 32 : 28 : 12 = 4 : 8 : 7 : 3 . . . . . . remove a factor of 4

D'E'F'G' ratios are 44 : 88 : 77 : 33 = 4 : 8 : 7 : 3 . . . . remove a factor of 11

The figure D'E'F'G' is a dilation of the figure DEFG. The ratios of the lengths of the corresponding sides are equal.​