Asked by Francis

find the equation of the perpendicular bisector of the line joining P(2, -4) to Q(-5,1)
A. 8y-14x 13=0
B. 8y-14x-13=0
C. 8y 14x-13=0
D. 8y 14x 13=0
Please I need someone to help me with this, with an explanatory workings.
Answered by Steve
the bisector goes through the midpoint of PQ. That is (-3/2,-3/2)

PQ has slope -5/7, so the perpendicular has slope 7/5

Now you have a point and a slope, so the line is

y+3/2 = 7/5 (x+3/2)
10y + 15 = 14x + 21
10y-14x-6 = 0

I suspect a typo. If you graph the two lines, you will see that PQ is indeed bisected by the calculated line.
Answered by Francis
So the question is wrong?
Answered by Steve
Yes. P and Q cannot be as given.
All of the choices have slope 7/4 or -7/4.
Answered by Francis
ok, can you pls direct me on how to work a similar question?
Answered by Steve
Uh, geez -- I believe I just did. Given two points, find the midpoint of the line connecting them.

Find the slope of that line, and take its negative reciprocal.

Now you have a point and a slope. Just write the equation of the bisecting line.
Answered by Francis
Alright, thanks.
Answered by Francis
Sorry one more thing, how do you get the slope?