Question

find the coordinates of the other endpoint of the segment of one endpoint is (-2,-7) and midpoint is (6,-10)

Answer 1

(14, - 13 )

Explanation:

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

[
`(1)/(2)` (x₁ + x₂ ),
`(1)/(2)` (y₁ + y₂ ) ]

let (x₁, y₁ ) = (- 2, - 7) and (x₂, y₂ ) = (x, y)

Using the midpoint formulae equate to the coordinates of the midpoint.

`(1)/(2)` (- 2 + x) = 6 ( multiply both sides by 2 )

- 2 + x = 12 ( add 2 to each side )

x = 14

and

`(1)/(2)` (- 7 + y ) = - 10 ( multiply both sides by 2 )

- 7 + y = - 20 ( add 7 to both sides )

y = - 13

Thus

coordinates of other endpoint = (14, - 13 )