the graph shows quadrilaterals ghdj and wxyz. is ghij congruent to wxyz? justify your answer. yes, because a rotation 180° around the origin maps ghij onto wxyz. yes, because a translation left 4 units and down 9 units maps ghij onto wxyz. no, because ∠j and ∠z do not have the same measure. no, because (overline{hi}) and (overline{xy}) do not have the same length.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{HI} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For points $ H(-3,5) $ and $ I(2,2) $, $ x_1=-3,y_1 = 5,x_2=2,y_2=2 $.
$$
\begin{align*}
d_{HI}&=\sqrt{(2-(-3))^2+(2 - 5)^2}\
&=\sqrt{(2 + 3)^2+(-3)^2}\
&=\sqrt{25 + 9}\
&=\sqrt{34}
\end{align*}
$$
## Step2: Calculate the length of $ \overline{XY} $
For points $ X(2,-5) $ and $ Y(-2,-2) $, $ x_1=2,y_1=-5,x_2=-2,y_2=-2 $.
$$
\begin{align*}
d_{XY}&=\sqrt{(-2 - 2)^2+(-2-(-5))^2}\
&=\sqrt{(-4)^2+(3)^2}\
&=\sqrt{16+9}\
&=\sqrt{25}\
& = 5
\end{align*}
$$

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

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QUESTION IMAGE

Question

Explanation:

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

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

Answer: