Question

The midpoint of segment AB is (-7, 10) and endpoint A is located at (3, -1). Find the other endpoint B. Show all work.

Answer 1

`B(-17,21)`

Explanation:

The midpoint of two points is the average of the x coordinates and the average of the y coordinates.

Given

A(3, -1)

and we let the other end point B be B(x,y)

and midpoint is (-7,10)

So, the average of 3 and x is -7, and

the average of -1 and y is 10

We can solve for x first:

`(3+x)/(2)=-7\\3+x=2*-7\\3+x=-14\\x=-14-3\\x=-17`

and now solving for y:

`(-1+y)/(2)=10\\-1+y=2*10\\-1+y=20\\y=20+1\\y=21`

So, the other point B is:

`B(-17,21)`