Question

Please help!!!
Identify the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7).

Answers are one of the following

1.y − 1 = −8(x − 7)
2.y − 7 = 8(x − 1)
3.y−1=−18(x−7)
4.y−1=18(x−7)

Answer 1

Answer:

$y-1=\frac{1}{8}\left(x-7\right)$ is the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7).

Step-by-step explanation:

The endpoints:

• B(6,9)

• C(8,−7)

Calculating the Midpoint M of BC:

$\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)$

$\left(x_1,\:y_1\right)=\left(6,\:9\right),\:\left(x_2,\:y_2\right)=\left(8,\:-7\right)$

The Midpoint M of BC $=\left(\frac{8+6}{2},\:\frac{-7+9}{2}\right)$

                                     $=\left(7,\:1\right)$

Calculating the slope of BC:

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(6,\:9\right),\:\left(x_2,\:y_2\right)=\left(8,\:-7\right)$

$m=\frac{-7-9}{8-6}$

$m=-8$

Given a line with slope $m$ then the slope of a

line  perpendicular to it is:

$m_{prependicular}=-\frac{1}{m}=-\frac{1}{-8}=\frac{1}{8}$

Equation of line using point-slope form

$y-y_1=m\left(x-x_1\right)$

$y-1=\frac{1}{8}\left(x-7\right)$        

     

Therefore, $y-1=\frac{1}{8}\left(x-7\right)$ is the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7).