Question

The midpoint of qr is m(5, 1). one endpoint is r(2, 2). find the coordinates of the other endpoint q. write the coordinates as decimals or integers.

Answer 1

q (8, 0 )

Explanation:

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

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

let (x₁, y₁ ) = r (2, 2 ) and (x₂, y₂ ) = q (x, y) ← to be found

equate each of the coordinates from the midpoint formula to the corresponding coordinates from m (5, 1 )

`(2+x)/(2)` = 5 ( multiply both sides by 2 to clear the fraction )

2 + x = 10 ( subtract 2 from each side )

x = 8

and

`(2+y)/(2)` = 1 ( multiply both sides by 2 to clear the fraction )

2 + y = 2 ( subtract 2 from both sides )

y = 0

the coordinates of q (8, 0 )