Question

The midpoint of a segment is 19,5) and one of the endpoints is (13,81 What are the coordinates of the otherendpoint

Answer 1

`(25,-71)`

Explanation:

Given

`(x,y) = (19,5)` --- midpoint

`(x_1,y_1) = (13,81)` --- end 1

Required

The other endpoint

Using midpoint formula, we have:

`(x,y) = 0.5 * [x_1 + x_2, y_1 + y_2]`

So, we have:

`(19,5) = 0.5 * [13 + x_2, 81 + y_2]`

Multiply both sides by 2

`2 * (19,5) = 2 * 0.5 * [13 + x_2, 81 + y_2]`

`(38,10) = [13 + x_2, 81 + y_2]`

By comparison:

`x_2 + 13 = 38` and
`y_2 + 81 = 10`

So:

`x_2 = 38 - 13`

`x_2 = 25`

and

`y_2 = 10 - 81`

`y_2 = - 71`

Henc, the other endpoint is:

`(25,-71)`