Math Help Needed!

Question:
Find the equation of the perpendicular bisector of the line joining (2, -5) and (-4, 3).
Give your answer in the form ax + bx + c = 0.

Answer: 3x - 4y - 1 = 0

I started by finding the midpoint of the line joining (2, -5) and (-4, 3):
( 1/2 (2+(-4) ) , 1/2 (-5+3)) = ( (1/2 * -2), (1/2 * -2) = (-1, -1)

Then I found the gradient of the line which came out as -4/3

Then I used -1 / (-4/3) = 3/4 to find the line perpendicular to the other which goes through its midpoint:
y - y1 = m (x - x1)
y - -1 = 3/4 (x - -1)
y + 1 = 3/4 (x + 1)
...
...
It doesnt simplify to the correct answer!

Anyone know whats wrong? is my method right? if so then it must be the working out so i can post more of it if needed

 

Yes it does

y + 1 = 3/4(x) + 3/4

y = 3/4(x) - 1/4

4y = 3x -1

3x - 4y -1 = 0

 

No, it does simplify properly. You just stopped too early, and in a different form.

4(y + 1) = 3(x + 1)
4y + 4 = 3x + 3
(4y + 4) - (4y + 4) = 3x + 3 - (4y - 4)
0 = 3x - 4y -1

(edit) Darn, beaten (/edit)

 

Ohh really? I just wasn't bothered to type it up but i did it on paper and it didn't
Anyway im sure i must have made i mistake somewhere so ill just go and correct it
Thanks