Question

here are the endpoints of the segments $overline{bc}$, $overline{fg}$, and $overline{jk}$.
$b(-1,6)$, $c(4,8)$
$f(1,-3)$, $g(-1,-8)$
$j(-7,3)$, $k(-2,1)$
follow the directions below.
1 find the length of each segment.
give an exact answer (not a decimal approximation).
$bc =$
$fg =$
$jk =$

Explanation:

Step1: Recall distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Step2: Calculate length of $BC$

$BC=\sqrt{(4 - (-1))^2+(8 - 6)^2}=\sqrt{25 + 4}=\sqrt{29}$

Step3: Calculate length of $FG$

$FG=\sqrt{(-1 - 1)^2+(-8 - (-3))^2}=\sqrt{4 + 25}=\sqrt{29}$

Step4: Calculate length of $JK$

$JK=\sqrt{(-2 - (-7))^2+(1 - 3)^2}=\sqrt{25 + 4}=\sqrt{29}$

Answer:

$BC=\sqrt{29}$
$FG=\sqrt{29}$
$JK=\sqrt{29}$