Question

The midpoint of a line segment is (4,2). If one of the endpoints is (-2,3), what is the other endpoint?

Answer 1

(10, 1 )

Explanation:

Using the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then

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

Calculate the coordinates of midpoint and equate each to the given midpoint

(x₁, y₁ ) = - 2, 3), let coordinates of other endpoint = (x, y ) , then

`(-3+x)/(2)` = 4 ( multiply both sides by 2 )

- 2 + x = 8 ( add 2 to both sides )

x = 10

and

`(3+y)/(2)` = 2 ( multiply both sides by 2 )

3 + y = 4 ( subtract 3 from both sides )

y = 1

coordinates of other endpoint are (10, 1 )