Find the equation of the perpendicular bisector of AB when A(-7,2) and B(3,4)

Question

asked Sep 18, 2021 47.2k views

1 Answer

Dr Casper Black · Answer 1 · 2021-09-24T01:45:20+0000

Given:

Two points are A(-7,2) and B(3,4).

To find:

The perpendicular bisector of AB.

Solution:

Slope formula:

m=(y_2-y_1)/(x_2-x_1)

Slope of AB is

m_1=(4-2)/(3-(-7))

m_1=(2)/(3+7)

m_1=(2)/(10)

m_1=(1)/(5)

Procut of slopes of perpendicular line is -1.

So, slope of perpendicular bisect is opposite of reciprocal of
(1)/(5) .

m_2=-5

Midpoint of AB is

$Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)$

$Midpoint=\left((-7+3)/(2),(2+4)/(2)\right)$

$Midpoint=\left((-4)/(2),(6)/(2)\right)$

$Midpoint=\left(-2,3\right)$

Slope of perpendicular bisector is -5 and it passes through (-2,3), so the equation of perpendicular bisector is

y-y_1=m(x-x_1)

where, m is slope.

y-3=-5(x-(-2))

y-3=-5(x+2)

y-3=-5x-10

Add 3 on both sides.

y=-5x-10+3

y=-5x-7

Therefore, the equation of perpendicular bisector is
.