Question

The midpoint of CD is E(-1,0). One endpoint is C(5,2). What are the coordinates of the other endpoint? A) D(-7, -2) B) D(-2, -7) C) D(-5, -2) D) D(2, 5)

Answer 1

A

Explanation:

use the midpoint formula to calculate E , then equate the x and y coordinates with the corresponding coordinates of point E (- 1, 0 )

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

let (x₁ , y₁ ) = C (5, 2 ) and (x₂, y₂ ) = D (
`x_(D)` ,
`y_(D)` )

E = (
`(5+x_(D) )/(2)` ,
`(2+y_(D) )/(2)` )

equate x and y coordinates to E (- 1, 0 )

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

5 +
`x_(D)` = - 2 ( subtract 5 from both sides )

`x_(D)` = - 7

similarly

`(2+y_(D) )/(2)` = 0 ( multiply both sides by 2 )

2 +
`y_(D)` = 0 ( subtract 2 from both sides )

`y_(D)` = - 2

coordinates of D (- 7, - 2 )