5. (overline{jk}) has endpoints (j(-3, -1)) and (k(0, 3)). (overline{rs}) has endpoints (r(1, 1)) and (s(4, 4)). is (overline{jk}congoverline{rs})? explain how you know.

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Accepted Answer

# Explanation:
## Step1: Calculate the length of $ \overline{JK} $
Use the distance formula $ d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $.
For $ J(-3,-1) $ and $ K(0,3) $, $ x_1=-3,y_1 = - 1,x_2=0,y_2 = 3 $.
$$
\begin{align*}
JK&=\sqrt{(0-(-3))^2+(3 - (-1))^2}\
&=\sqrt{(0 + 3)^2+(3+1)^2}\
&=\sqrt{3^2+4^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $ \overline{RS} $
For $ R(1,1) $ and $ S(4,4) $, $ x_1 = 1,y_1=1,x_2 = 4,y_2=4 $.
$$
\begin{align*}
RS&=\sqrt{(4 - 1)^2+(4 - 1)^2}\
&=\sqrt{3^2+3^2}\
&=\sqrt{9+9}\
&=\sqrt{18}\
&=3\sqrt{2}\approx4.24
\end{align*}
$$

# Answer:
Since $ JK = 5$ and $ RS=3\sqrt{2}\approx4.24$, $ JK
eq RS$, so $ \overline{JK}
ot\cong\overline{RS}$

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QUESTION IMAGE

Question

Explanation:

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

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

Answer: