Question

The midpoint of a sègment is (6,-4) and one endpoint is (13,-2). Find the coordinates of the other endpoint.

Answer 1

(- 1, - 6 )

Explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

(
`(x_(1)+x_(2) )/(2)` ,
`(y_(1)+y_(2) )/(2)` ) ← midpoint formula

Use this formula on the endpoints and equate to the coordinates of the midpoint.

let the other endpoint = (x, y) , then

`(13+x)/(2)` = 6 ( multiply both sides by 2 )

13 + x = 12 ( subtract 13 from both sides )

x = - 1

`(-2+y)/(2)` = - 4 ( multiply both sides by 2 )

- 2 + y = - 8 ( add 2 to both sides )

y = - 6

The coordinates of the other endpoint are (- 1, - 6 )

Answer 2

let other one be (x,y)

We know midpoint formula

`\boxed{\sf (x,y)=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)}`

`\\ \sf\longmapsto (6,-4)=\left((13+x)/(2),(-2+y)/(2)\right)`

`\\ \sf\longmapsto (13+x)/(2)=6`

`\\ \sf\longmapsto 13+x=12`

`\\ \sf\longmapsto x=12-13`

`\\ \sf\longmapsto x=-1`

And

`\\ \sf\longmapsto (-2+y)/(2)=-4`

`\\ \sf\longmapsto -2+y=-8`

`\\ \sf\longmapsto y=-8+2`

`\\ \sf\longmapsto y=-6`