Question

Given the midpoint (5,8) and that one of the endpoints is (-2. 6), find the other endpoint

of the segment.

Answer 1

Answer:

(12, 10 )

Explanation:

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

[ (x₁ + x₂ ), (y₁ + y₂ ) ]

let (x, y) be the coordinates of the other endpoint then use the midpoint formula and equate to the coordinates of the midpoint.

(x₁, y₁ ) = (- 2, 6) and (x₂, y₂ ) = (x, y), then

(- 2 + x) = 5 ( multiply both sides by 2 )

- 2 + x = 10 ( add 2 to both sides )

x = 12

(6 + y) = 8 ( multiply both sides by 2 )

6 + y = 16 ( subtract 6 from both sides )

y = 10

Thus

The other endpoint is (12 ,10)

Answer 2

(12, 10 )

Explanation:

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

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

let (x, y) be the coordinates of the other endpoint then use the midpoint formula and equate to the coordinates of the midpoint.

(x₁, y₁ ) = (- 2, 6) and (x₂, y₂ ) = (x, y), then

`(1)/(2)`(- 2 + x) = 5 ( multiply both sides by 2 )

- 2 + x = 10 ( add 2 to both sides )

x = 12

`(1)/(2)`(6 + y) = 8 ( multiply both sides by 2 )

6 + y = 16 ( subtract 6 from both sides )

y = 10

Thus

The other endpoint is (12, 10 )