Question

write the equation of the perpendicular bisector of the segment joining A(-5,4) and B(3,-6)

Answer 1

mid point = ( -1,-1) ===> slope = -10/8=-5/4 ==> slope of perpendicuar = 4/5 ===> equation is y=4/5 x+b ===> -1=-4/5+ b ===> b=-1/5 ==> y =4/5 x-1/5

Answer 2

You need to find the mid points first, the mid points for the segment are \((-1,-1)\)
Then Slope of the Segment which is \(\frac{-10}{8}\)
Slope of the perpendicular line would be \(\frac{8}{10}\)
Now you have you're equation \(y = \frac{8}{10}*x + c\)
Now put the mid point to determine the C.
And you have your equation :D