Question

The midpoint of EF is M(4, 10). One endpoint is E(2, 6). Find the coordinates of the other endpoint F.

Answer 1

Well, to get from M to E you subtract two from the x, and 4 from the y. So go the other way, and add two to the x and 4 to the y. You get (6, 14)
This is because each endpoint is equidistant from the midpoint.

Answer 2

Other point F ( 6 ,14).

Explanation:

Given : The midpoint of EF is M(4, 10). One endpoint is E(2, 6).

To find : Find the coordinates of the other endpoint F.

Solution : We have given that

Line EF have mid point M ( 4 ,10)

One end point E ( 2 ,6) .

Let other point F (
`x_(2) ,y_(2)`)

Mid point segment formula ( M) :
`((x_(1)+x_(2))/(2) , (y_(1)+y_(2))/(2))`.

`(x_(1)+x_(2))/(2)` = 4

Plug
`x_(1)` = 2.

`(2+x_(2))/(2)` = 4

On multiplying both side by 2

2 +
`x_(2)` = 8

`x_(2)` = 8- 2

`x_(2)` = 6.

`(y_(1)+y_(2))/(2)` = 10.

Plug
`y_(1)` = 6.

`(6+y_(2))/(2)` = 10.

On multiplying both side by 2

6 +
`y_(2)` = 20

`y_(2)` = 20 - 6

`y_(2)` = 14.

Therefore, Other point F ( 6 ,14).