b(6, -7), c(-2, -8)
f(-7, 0), g(-8, 8)
j(5, 6), k(6, -2)
follow the directions below.
(a) find the length of each segment.
give an exact answer (not a decimal approximation).
bc =
fg =
jk =
(b) check all statements that are true below.
□ \overline{bc} \cong \overline{fg}
□ \overline{bc} \cong \overline{jk}
□ \overline{fg} \cong \overline{jk}
□ none of these are true

Question

Accepted Answer

# Explanation:
## Step1: Use 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 $BC$
For $B(6,-7)$ and $C(-2,-8)$, $x_1 = 6,y_1=-7,x_2=-2,y_2 = -8$.
$$
\begin{align*}
BC&=\sqrt{(-2 - 6)^2+(-8+7)^2}\
&=\sqrt{(-8)^2+(-1)^2}\
&=\sqrt{64 + 1}\
&=\sqrt{65}
\end{align*}
$$
## Step3: Calculate $FG$
For $F(-7,0)$ and $G(-8,8)$, $x_1=-7,y_1 = 0,x_2=-8,y_2 = 8$.
$$
\begin{align*}
FG&=\sqrt{(-8 + 7)^2+(8-0)^2}\
&=\sqrt{(-1)^2+8^2}\
&=\sqrt{1 + 64}\
&=\sqrt{65}
\end{align*}
$$
## Step4: Calculate $JK$
For $J(5,6)$ and $K(6,-2)$, $x_1 = 5,y_1=6,x_2=6,y_2=-2$.
$$
\begin{align*}
JK&=\sqrt{(6 - 5)^2+(-2 - 6)^2}\
&=\sqrt{1^2+(-8)^2}\
&=\sqrt{1+64}\
&=\sqrt{65}
\end{align*}
$$

# Answer:
- $BC=\sqrt{65}$
- $FG=\sqrt{65}$
- $JK=\sqrt{65}$
- For part (b): $\overline{BC}\cong\overline{FG}$, $\overline{BC}\cong\overline{JK}$, $\overline{FG}\cong\overline{JK}$ are all true.

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QUESTION IMAGE

Question

Explanation:

Step1: Use the distance formula

Step2: Calculate \(BC\)

Step3: Calculate \(FG\)

Step4: Calculate \(JK\)

Answer: