the graph shows quadrilaterals klmn and rstu. is klmn congruent to rstu? justify your answer. yes, because a translation left 11 units and up 8 units maps klmn onto rstu. yes, because a rotation 180° around the origin maps klmn onto rstu. no, because ∠k and ∠r do not have the same measure. no, because (overline{lm}) and (overline{st}) do not have the same length.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{LM} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For points $ L(7,-7) $ and $ M(1,-3) $, $ x_1 = 7,y_1=-7,x_2 = 1,y_2=-3 $.
$$
\begin{align*}
d_{LM}&=\sqrt{(1 - 7)^2+(-3+7)^2}\
&=\sqrt{(-6)^2 + 4^2}\
&=\sqrt{36 + 16}\
&=\sqrt{52}
\end{align*}
$$
## Step2: Calculate the length of $ \overline{ST} $
For points $ S(-3,1) $ and $ T(-8,5) $, $ x_1=-3,y_1 = 1,x_2=-8,y_2 = 5 $.
$$
\begin{align*}
d_{ST}&=\sqrt{(-8 + 3)^2+(5 - 1)^2}\
&=\sqrt{(-5)^2+4^2}\
&=\sqrt{25 + 16}\
&=\sqrt{41}
\end{align*}
$$
Since $ \sqrt{52}
eq\sqrt{41} $, $ \overline{LM}$ and $ \overline{ST}$  do not have the same length.

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

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QUESTION IMAGE

Question

Explanation:

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

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

Answer: