Question

Write an equation of the perpendicular bisector of the segment joining a(-2,3) and b(4,-5).

Answer 1

Answer:

C) 3x - 4y = 7

Step-by-step explanation:

The midpoint of AB is

M( (-2 + 4)/2, (-5 + 3)/2 ) = M(1, -1)

Line AB has slope:

(3 - (-5))/(-2 - 4) = 8/(-6) = -4/3

Slopes of perpendicular lines are negative reciprocals.

A perpendicular to line AB has slope 3/4.

The perpendicular to line AB that passes through the midpoint of segment AB is the line we want.

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

$y - (-1) = \dfrac{3}{4}(x - 1)$

$y + 1 = \dfrac{3}{4}(x - 1)$

$4y + 4 = 3(x - 1)$

$4y + 4 = 3x - 3$

$3x - 4y = 7$

Answer 2

Answer:

C

Step-by-step explanation:

Segment joining a and b

m = 8/(-6) =-4/3

For that of the perpendicular bisector...

m = 3/4

Midpoint of Segment joining a and b

([-2+4]/2 , [3-5]/2)

=(1, -1)

y=mx+c

-1=(3/4)(1)+c

c= -7/4

y=3x/4 - 7/4

4y=3x - 7

3x-4y = 7