the graph shows quadrilaterals defg and nopq. is defg congruent to nopq? justify your answer. yes, because a reflection across the y - axis maps defg onto nopq. yes, because a translation right 12 units maps defg onto nopq. no, because $ \overline { ef } $ and $ \overline { op } $ do not have the same length. no, because $ \overline { gd } $ and $ \overline { qn } $ do not have the same length.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{GD} $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $. For points $ G(-2,5) $ and $ D(-6,2) $, $ x_1=-2,y_1 = 5,x_2=-6,y_2=2 $.
$$
\begin{align*}
d_{GD}&=\sqrt{(-6+2)^2+(2 - 5)^2}\
&=\sqrt{(-4)^2+(-3)^2}\
&=\sqrt{16 + 9}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $ \overline{QN} $
For points $ Q(9,5) $ and $ N(5,2) $, $ x_1=9,y_1 = 5,x_2=5,y_2=2 $.
$$
\begin{align*}
d_{QN}&=\sqrt{(5 - 9)^2+(2 - 5)^2}\
&=\sqrt{(-4)^2+(-3)^2}\
&=\sqrt{16+9}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step3: Calculate the length of $ \overline{EF} $
For points $ E(-9,5) $ and $ F(-5,8) $, $ x_1=-9,y_1 = 5,x_2=-5,y_2=8 $.
$$
\begin{align*}
d_{EF}&=\sqrt{(-5 + 9)^2+(8 - 5)^2}\
&=\sqrt{(4)^2+(3)^2}\
&=\sqrt{16+9}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step4: Calculate the length of $ \overline{OP} $
For points $ O(3,5) $ and $ P(6,8) $, $ x_1=3,y_1 = 5,x_2=6,y_2=8 $.
$$
\begin{align*}
d_{OP}&=\sqrt{(6 - 3)^2+(8 - 5)^2}\
&=\sqrt{(3)^2+(3)^2}\
&=\sqrt{9+9}\
&=\sqrt{18}\
&=3\sqrt{2}\approx4.24
\end{align*}
$$

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

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QUESTION IMAGE

Question

Explanation:

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

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

Step3: Calculate the length of \( \overline{EF} \)

Step4: Calculate the length of \( \overline{OP} \)

Answer: