The midpoint of segment AB is M(−2,2). If A is located at (−5,7) find the coordinates of the endpoint B.

Solution
Since we do not know the coordinates of point B we will use (x2,y2) as our coordinate. We will use our given point A and B and substitute into the midpoint formula. We would start with

M=(x1+x22,y1+y22)

Now let’s substitute in our given values.

( , 2)=((−5+x2)2,(7+y2)2)

Find x2 and y2
We will now set up two equations to solve for our two unknowns of x2 and y2.

( +x2)/2=

We will first want to multiply by 2 on both sides and will get

−5+x2=−4

Adding 5 to both sides we get

x2=

This is the x coordinate of point B. Now we will set up the equation to solve for y2

( +y2)/2=

We will first want to multiply by 2 on both sides and will get

+y2=

y2=

This is the y-coordinate of point B. The coordinates of point B are
( , )