Question

A line segment has a midpoint of (7, 1/2 )

If one endpoint is (3,2), what is the other endpoint?

Answer 1

(11, -1)

Explanation:

We get the midpoint by "averaging" the x-coordinates and y-coordinates.

One endpoint is (3,2) and let the other end point be (x,y). Thus, we can say:

• average of 3 and x is 7 [x coordinate of midpoint], and
• average of 2 and y is 1/2 [y coordinate of midpoint]

Let's do the math:

`(3+x)/(2)=7\\3+x=7*2\\3+x=14\\x=14-3\\x=11`

And

`(2+y)/(2)=(1)/(2)\\2(2+y)=2\\4+2y=2\\2y=2-4\\2y=-2\\y=(-2)/(2)\\y=-1`

The other endpoint coordinates is thus:

(11, -1)