Question

The midpoint of MN is point P at (-4, 6). If point M is at (8, -2), what are the coordinates of point N?

O (-16, 14)
O (-10,5)
O (22)
O (6,2)

Answer 1

N(- 16, 14 )

Explanation:

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

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

Use this formula and equate to the coordinates of the midpoint P

let the coordinates of N = (x, y ), then

`(1)/(2)`(8 + x ) = - 4 ( multiply both sides by 2 )

8 + x = - 8 ( subtract 8 from both sides )

x = - 16

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

- 2 + y = 12 ( add 2 to both sides )

y = 14

Thus

coordinates of N = (- 16, 14 )