Point A has coordinates (-24, -54) Point B has coordinates (40, -46)
Find the equation of the perpendicular bisector of line AB.
ANSWER ASAP

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the midpoint of the line segment

Midpoint: where the coordinates of the endpoints are and

Plug in the endpoints (-24, -54) and (40, -46)

Therefore, the midpoint of line AB is (8,-50).

2) Determine the slope of the line segment

This will help us find the equation of the perpendicular bisector.

slope = where two given points are and

Plug in the endpoints (-24, -54) and (40, -46)

Therefore, the slope of line AB is .

3) Determine the slope of the perpendicular bisector

Because perpendicular lines always have slopes that are negative reciprocals, the slope of the perpendicular bisector is -8 (the negative reciprocal of 1/8). Plug this slope into :

4) Determine the y-intercept (b) of the perpendicular bisector

Recall that we found the midpoint of line AB, (8,-50). The perpendicular bisector passes through this point. Plug (8,-50) into and solve for b:

Add 64 to both sides to isolate b

Therefore, the y-intercept of the line is 14. Plug this back into :

I hope this helps!

lo ; )