1. ## Perpendicular Bisector

Hey guys, something that is probably easy for you is lurking below:

We're working on Perpendicular bisectors at the minute, and all my working is perfectly right, but I still seem to be getting the wrong answer. I need to get a hang of it by tomorrow morning (It's currently 10pm) as we are moving on and won't be covering it again.

The exercises which we are using are:

1) Find the equation of the perpendicular bisector of the line joining each pair of points:

A(5, -7) and J (6,4)

I know that I need to get to y-b = m(x-a) and to do this I must first need to figure out the middle point using:

x1+x2 / 2

y1+y2
/ 2

Which will fill in a and b of y-b = m(x-a)

I then need to use:

m = y2-y1 / x2-x1

then using the answer to this, I then need to use m1 x m2 = -1 to be able to fill in M in the y-b = m(x-a).

I then need to switch it around so that x + y + n = 0
(where n is number)

But I still seem to be getting the wrong answer. If someone could show me the solution to the above one, I might be able to figure out where I am going wrong.

Find the equation of the perpendicular bisector of each side of a triangle with vertices:

P (1, 3), R (0, 4) and Q (5, 2)

Any help would be much appreciated. I think that once I get a grasp of where I am going wrong with the first part, I should be able to figure out the second question.

Thank you so much in advance!

2. Originally Posted by Mathy
1) Find the equation of the perpendicular bisector of the line joining each pair of points:

A(5, -7) and J (6,4)
Find the midpoint:
$\displaystyle x = \frac{5 + 6}{2} = \frac{11}{2}$

$\displaystyle y = \frac{-7 + 4}{2} = -\frac{3}{2}$

Now find the slope of the line connecting points A and J:
$\displaystyle m = \frac{-7 - 4}{5 - 6} = 11$

So the line we want has a slope of $\displaystyle -\frac{1}{11}$ and intersects the point $\displaystyle \left ( \frac{11}{2}, -\frac{3}{2} \right )$.

So
$\displaystyle y = mx + b$

$\displaystyle -\frac{3}{2} = -\frac{1}{11} \cdot \frac{11}{2} + b$

So
$\displaystyle b = -\frac{3}{2} + \frac{1}{11} \cdot \frac{11}{2}$

$\displaystyle b = -\frac{3}{2} + \frac{1}{2} = -1$

$\displaystyle y = -\frac{1}{11}x - 1$