Question

NEED HELP ASAP! PLEASE1

Determine the equation of the perpendicular bisector of the segment with endpoints (–5, 3) and (5, 5).

A.) y= 1/5x+4
B.) y=-5x
C.)y=-5x+4
D.)1/5x

Answer 1

C. y = -5x + 4

Explanation:

segment with endpoints (–5, 3) and (5, 5)

Slope m = (y2-y1)/(x2-x1)

m = (5 - 3)/(5 - -5) = 2/10 = 1/5

Perpendicular lines have slopes that are negative reciprocals of one another. So slope of bisector is -5

Bisector intersects the segment at midpoints so

x = (Xa + Xb)/2 = (-5 + 5)/2 = 0/2 = 0

y = (Ya + Yb)/2 = (3 + 5)/2 = 8/2 = 4

so midpoint is (0,4)

using slope = -5

y = mx + b

4 = -5(0) + b

b = 4

then y = -5x + 4