here are the endpoints of the segments $ \overline { b c } $, $ \overline { f g } $, and $ \overline { j k } $.
$ b ( - 7,2 ), c ( - 4,7 ) $
$ f ( - 2,1 ), g ( 1, - 4 ) $
$ j ( 1,7 ), k ( 7,6 ) $
follow the directions below.
(a) find the length of each segment.
give an exact answer (not a decimal approximation).
$ b c = $
$ f g = $
$ j k = $

Question

Accepted Answer

# Explanation:
## Step1: Recall the distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
## Step2: Calculate the length of $BC$
For $B(-7,2)$ and $C(-4,7)$, $x_1=-7,y_1 = 2,x_2=-4,y_2 = 7$.
$$
\begin{align*}
BC&=\sqrt{(-4-(-7))^2+(7 - 2)^2}\
&=\sqrt{(3)^2+(5)^2}\
&=\sqrt{9 + 25}\
&=\sqrt{34}
\end{align*}
$$
## Step3: Calculate the length of $FG$
For $F(-2,1)$ and $G(1,-4)$, $x_1=-2,y_1 = 1,x_2=1,y_2=-4$.
$$
\begin{align*}
FG&=\sqrt{(1-(-2))^2+(-4 - 1)^2}\
&=\sqrt{(3)^2+(-5)^2}\
&=\sqrt{9+25}\
&=\sqrt{34}
\end{align*}
$$
## Step4: Calculate the length of $JK$
For $J(1,7)$ and $K(7,6)$, $x_1=1,y_1 = 7,x_2=7,y_2 = 6$.
$$
\begin{align*}
JK&=\sqrt{(7 - 1)^2+(6 - 7)^2}\
&=\sqrt{(6)^2+(-1)^2}\
&=\sqrt{36+1}\
&=\sqrt{37}
\end{align*}
$$

# Answer:
$BC=\sqrt{34}$, $FG=\sqrt{34}$, $JK=\sqrt{37}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the distance formula

Step2: Calculate the length of \(BC\)

Step3: Calculate the length of \(FG\)

Step4: Calculate the length of \(JK\)

Answer: