the graph shows quadrilaterals mnop and wxyz. is mnop congruent to wxyz? justify your answer. yes, because a translation left 4 units and up 9 units followed by a reflection across the x - axis maps mnop onto wxyz. yes, because a rotation 90° counterclockwise around the origin followed by a translation down 9 units maps mnop onto wxyz. no, because $ \overline { p m } $ and $ \overline { z w } $ do not have the same length. no, because $ \angle o $ and $ \angle y $ do not have the same measure.

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Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{PM} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For points $ P(-5,-3) $ and $ M(-2,-2) $, $ x_1=-5,y_1 = - 3,x_2=-2,y_2=-2 $.
$$
\begin{align*}
d_{PM}&=\sqrt{(-2+5)^2+(-2 + 3)^2}\
&=\sqrt{(3)^2+(1)^2}\
&=\sqrt{9 + 1}\
&=\sqrt{10}
\end{align*}
$$
## Step2: Calculate the length of $ \overline{ZW} $
For points $ Z(-9,-6) $ and $ W(-7,-8) $, $ x_1=-9,y_1=-6,x_2=-7,y_2=-8 $.
$$
\begin{align*}
d_{ZW}&=\sqrt{(-7 + 9)^2+(-8+6)^2}\
&=\sqrt{(2)^2+(-2)^2}\
&=\sqrt{4+4}\
&=\sqrt{8}=2\sqrt{2}
\end{align*}
$$
Since $ \sqrt{10}
eq2\sqrt{2} $, $ \overline{PM}
eq\overline{ZW} $. Congruent figures have all corresponding sides equal.

# Answer:
No, because $ \overline{PM} $ and $ \overline{ZW} $ do not have the same length.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \( \overline{PM} \)

Step2: Calculate the length of \( \overline{ZW} \)

Answer: