Question

The midpoint of CD is M=(-2, 6). One endpoint is C=(3, 8).

Find the coordinates of the other endpoint, D.
M (-2, 6)
D (?.?)
C (3.8)

Answer 1

D (- 7, 4 )

Explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the coordinates of midpoint (M) are

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

let (x₁, y₁ ) = C (3, 8 ) and (x₂, y₂ ) = D (x, y ) with M = (- 2, 6 )

use the midpoint formula and equate the x/y coordinates to the corresponding x/y coordinates of M , that is

`(3+x)/(2)` = - 2 ( multiply both sides by 2 to clear the fraction )

3 + x = - 4 ( subtract 3 from both sides )

x = - 7

and

`(8+y)/(2)` = 6 ( multiply both sides by 2 to clear the fraction )

8 + y = 12 ( subtract 8 from both sides )

y = 4

coordinates of D = (- 7, 4 )