Question

The figure PQRS is a parallelogram. Point M is the midpoint of PS.

What is the length of QY?

6 units
8 units
12 units
16 units

Answer 1

Hey Modelnick333, I have never answered one of these before, so I may not do this exactly right, and furthermore, I majored in Business and haven't used Geometry in nearly 20years, but I believe I have your answer.

Since PSRQ is a parallelogram, we know that SR and PQ are equal. Thus, PQ = 4units. The question then is what is YP? Being that I am a business major, and assuming this drawing is to scale, I would just eyeball it at this point and guess 8units. However, math wants you to prove things, so let's try to do that.

Since M is the midpoint of PS and YR, know we know that the triangle MSR and YMP are the same. Thus, line YP is = to SR, meaning it is also 4units. Therefore, line YQ = YP + PQ = 8units.

Does this help?

Answer 2

That's understandable. Thanks a lot for your help! :)

Answer 3

Sure thing modelnick333!