Question

parallelogram mnpq was dilated to create parallelogram mnpq. which statements are true about the parallelograms? select three options. the length of side mn is 2 units. the length of side mn is 5 units. the image is smaller than the pre - image. sides mq and mq both have the same slope, 1. the scale factor is \\(\frac{2}{5}\\).

Explanation:

Step1: Get coordinates of MN

M(2,-2), N(4,-2). Length $MN=|4-2|=2$ units.

Step2: Get coordinates of M'N'

M'(3,-5), N'(8,-5). Length $M'N'=|8-3|=5$ units.

Step3: Compare image and pre-image

M'N' (5) > MN (2), so image is larger.

Step4: Calculate slope of MQ and M'Q'

MQ: M(2,-2), Q(1,-3). Slope $\frac{-3-(-2)}{1-2}=\frac{-1}{-1}=1$.
M'Q': M'(3,-5), Q'(1,-7). Slope $\frac{-7-(-5)}{1-3}=\frac{-2}{-2}=1$.

Step5: Find scale factor

Scale factor = $\frac{M'N'}{MN}=\frac{5}{2}$ (not $\frac{2}{5}$).

Answer:

A. The length of side MN is 2 units, B. The length of side M'N' is 5 units, D. Sides MQ and M'Q' both have the same slope, 1