Determine whether one figure is a dilation of the other ?

Question

Determine whether one figure is a dilation of the other. Justify your answer: Quadrilateral DEFG has sides measuring 16m, 28m, 24m, and 20m. Quadrilateral D'E'F'G' has sides measuring 20m, 35m, 30m, and 25m

Answer 1

And BTW, Nancy has posted several questions about dilations in a short time frame, so it's safe to say that she's unloading her homework here.  It doesn't help her to answer here, since people who want us to do their homework typically don't care about understanding anything, but rather are taking advantage of the shortest path to getting it done.  Always check to make sure you're not responding to a serial poster.  Otherwise you unintentionally reverse help and harm.

Answer 2

To be a dilation, the second quadrilateral would have to have sides that are changed by the same factor as every other side.

 

Since the sides are listed in order, we can look at them individually.  The first question is, what is the ratio of the first two set of sides.  In other words, what is D'/D?  

 

D'/D = 20/16 = 5/4 = 1.25.  So D' = 1.25*D.

 

If all the other sides have the same relationship (E' = 1.25*E, and so on), the quadrilateral is probably a dilation (assuming the centers are the same and the shape is expanded evenly around the center; otherwise, the two quadrilaterals may technically be merely similar; but I think the question means us to assume that).