the graph shows triangles mno and tuv. is mno congruent to tuv? justify your answer. yes, because a reflection across the y - axis maps mno onto tuv. yes, because a rotation 90° counterclockwise around the origin maps mno onto tuv. no, because ∠n and ∠u do not have the same measure. no, because (overline{mn}) and (overline{tu}) do not have the same length.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{MN} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For points $ M(1,2) $ and $ N(9,4) $, $ x_1 = 1,y_1 = 2,x_2 = 9,y_2 = 4 $.
$$
\begin{align*}
d_{MN}&=\sqrt{(9 - 1)^2+(4 - 2)^2}\
&=\sqrt{8^2+2^2}\
&=\sqrt{64 + 4}\
&=\sqrt{68}
\end{align*}
$$
## Step2: Calculate the length of $ \overline{TU} $
For points $ T(-2,2) $ and $ U(-10,5) $, $ x_1=-2,y_1 = 2,x_2=-10,y_2 = 5 $.
$$
\begin{align*}
d_{TU}&=\sqrt{(-10+2)^2+(5 - 2)^2}\
&=\sqrt{(-8)^2+3^2}\
&=\sqrt{64+9}\
&=\sqrt{73}
\end{align*}
$$
Since $ \sqrt{68}
eq\sqrt{73} $, $ \overline{MN}
eq\overline{TU} $. Congruent triangles have all corresponding sides equal.

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

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QUESTION IMAGE

Question

Explanation:

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

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

Answer: