Question

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

Explanation:

Step1: Check side lengths ratio

Assume grid units: MN length = 5, QP length = 6; AB length = 2, CD length = 2.
$\frac{AB}{MN} = \frac{2}{5}$, $\frac{CD}{QP} = \frac{2}{6} = \frac{1}{3}$. Ratios differ.

Step2: Evaluate dilation condition

Dilation requires all corresponding sides to have the same scale factor. Here, ratios are not equal.

Answer:

No, because AB is $\frac{2}{5}$ the length MN but CD is $\frac{1}{3}$ the length QP.