First, you will need to know the midpoint formula:

M=((x_{1}+x_{2})/2 , (y_{1}+y_{2})/2)

Let us call A = (x_{1}, y_{1}). This means that x_{1}=-1 and y_{1}=-8.

We know that the midpoint, M, is (6, -1).

B will be the unknown point, (x_{2}, y_{2}).

Therefore, we must plug in what we know:

(6, -1) = ((-1+x_{2})/2 , (-8+y_{2})/2).

From here, we will create two equations. One will help us to solve for x_{2}, and the other will help us to solve for y_{2}. We will create the two equations by setting the x value on the left hand side equal to the x value on the right hand side:

6 = (-1+x_{2})/2 {multiplying both sides by 2 gives us}

12 = -1 + x_{2} {adding 1 to both sides gives us the value for x_{2}}

x_{2} = 13

Now we will need to find y_{2} using the same method (setting the value for y on the left hand side equal to the value for y on the right hand side).

-1 = (-8+y_{2})/2 {multiplying both sides by 2 gives us}

-2 = -8 + y_{2} {adding 8 to both sides gives us the value for y_{2}}

y_{2} = 6

Therefore, we know that point B is (13, 6). That is the answer.

To check your answer, plug A and B back into the midpoint formula:

M = ((-1 + 13)/2 , (-8 + 6)/2)

M = ((12/2) , (-2/2))

M = (6,-1)

which is correct!

Christine M.

08/27/13