Question

Identify the equation in point-slope form for the perpendicular bisector of the segment with endpoints J(−24,−4) and K(−4,6).

Answer 1

Given:

Endpoints of a segment are J(−24,−4) and K(−4,6).

To find:

The equation in point-slope form for the perpendicular bisector of JK.

Solution:

Slope of JK is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{6-(-4)}{-4-(-24)}$

$m=\dfrac{6+4}{-4+24}$

$m=\dfrac{10}{20}$

$m=\dfrac{1}{2}$

Product of slopes of two perpendicular lines is -1. So, product of perpendicular line of JK is -2.

Perpendicular bisector of JK passes through the midpoint of JK.

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$Midpoint=\left(\dfrac{-24-4}{2},\dfrac{-4+6}{2}\right)$

$Midpoint=\left(\dfrac{-28}{2},\dfrac{2}{2}\right)$

$Midpoint=\left(-14,1\right)$

Point slope form:

$y-y_1=m(x-x_1)$

where, m is slope.

Perpendicular bisector of JK passes through (-14,1) with slope -2. So, the point slope form of JK is

$y-1=-2(x-(-14))$

$y-1=-2(x+14)$

Therefore, the correct option is D.