Question

is trapezoid abdc the result of a dilation of trapezoid mnpq by a scale factor of \\(\frac{2}{5}\\)? why or why not?
yes, because sides ab and cd are parallel to sides mn and qp.
yes, because ab and cd are each \\(\frac{2}{5}\\) the lengths mn and qp.
no, because sides ab and cd have different slopes from sides mn and qp.

Explanation:

Step1: Recall Dilation Properties

Dilation preserves parallelism (slopes of sides remain equal) and scales side lengths by the scale factor. For trapezoid \(MNPQ\) and \(ABDC\), check if \(AB \parallel CD\) (same as \(MN \parallel QP\) in original) and if side lengths of \(ABDC\) are \(\frac{2}{5}\) of \(MNPQ\).

Step2: Analyze Options

• First option: Incorrect, dilation preserves parallelism (slopes same).
• Second option: Correct. Dilation scales lengths (so \(AB, CD\) should be \(\frac{2}{5}\) of \(MN, QP\)) and preserves parallelism (so \(AB \parallel CD\) as \(MN \parallel QP\)).
• Third option: Incorrect, reason about length scaling, not just parallelism.

Answer:

The middle option (Yes, because \(AB\) and \(CD\) are each \(\frac{2}{5}\) the lengths \(MN\) and \(QP\))