Question

is trapezoid abdc the result of a dilation of trapezoid mnpq by a scale factor of 2 5? why or why not? yes, because ab and cd are each 2 5 the lengths of mn and qp. yes, because sides ab and cd are parallel to sides mn and qp. no, because ab is 2 5 the length of mn but cd is 1 3 the length of qp. no, because sides ab and cd have different slopes from sides mn and qp.

Explanation:

Step1: Recall dilation properties

In a dilation, corresponding - sides of the pre - image and the image are proportional and parallel.

Step2: Check side - length ratios and parallelism

For two polygons to be a dilation of each other, all corresponding sides must be in the same ratio. If one pair of corresponding sides has a different ratio than the others, it is not a dilation. Also, corresponding sides of dilated figures are parallel.
If the lengths of corresponding sides are not in the same ratio, the figures are not a dilation.

Answer:

No, because the length MN is \(2\frac{5}{2}\) and the length CD is \(1\frac{3}{2}\), and the ratio of their lengths is not consistent with the ratio of other corresponding sides. So the answer is the option that says "No" due to inconsistent side - length ratios.