the graph shows triangles pqr and tuv. is pqr congruent to tuv? justify your answer. yes, because a reflection across the line y = -x maps pqr onto tuv. yes, because a rotation 180° around the origin maps pqr onto tuv. no, because ∠r and ∠v do not have the same measure. no, because (overline{pq}) and (overline{tu}) do not have the same length.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{PQ} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For $ P(9,3) $ and $ Q(6,7) $, $ x_1 = 9,y_1 = 3,x_2 = 6,y_2 = 7 $.
$$
\begin{align*}
d_{PQ}&=\sqrt{(6 - 9)^2+(7 - 3)^2}\
&=\sqrt{(- 3)^2+4^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $ \overline{TU} $
For $ T(-2,-8) $ and $ U(-7,-6) $, $ x_1=-2,y_1 = - 8,x_2=-7,y_2=-6 $.
$$
\begin{align*}
d_{TU}&=\sqrt{(-7+2)^2+(-6 + 8)^2}\
&=\sqrt{(-5)^2+2^2}\
&=\sqrt{25+4}\
&=\sqrt{29}
\end{align*}
$$

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

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QUESTION IMAGE

Question

Explanation:

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

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

Answer: