Question

Line segment NY has endpoints N(-11,5) and Y(5,-7). What is the equation of the perpendicular bisector of line NY?

Answer 1

The first thing to do is find the slope of the given line m = (y2-y1)/(x2-x1). We need to find the slope because it is required to find the slope of the perpendicular line.

m = (-7-5)/(5+11) = -12/16 = -3/4

Now we find the midpoint of the line, this is where the perpendicular bisector be. Using the Midpoint equation

M=((x1+x2)/2,(y1+y2)/2)
M=((-11+5)/2, (5-7)/2)
M=(-6/2, -2/2)
M=(-3,-1)

Now that we have the slope and midpoint we can find the perpendicular bisector. A line is perpendicular to another if, when you multiply their slopes together they equal -1. To do this we simply invert the numerator and denominator of our current slope and flip the sign from negative to positive.

So, -3/4 becomes positive 4/3 for our new line. So for our perpendicular line we now know two things, the slope and a point on it (the bisector point). To find the equation of the line we need to plug the known point and slope into the equation y = mx + b and solve for b.

-1 = 4/3(-3) + b
-1 = -4 + b
b = -1 + 4
b = 3

Now we can build our equation for our perpendicular line

y = 4/3x + 3