Question

The midpoint of PR is (-6,9). P=(-15,4)

What are the coordinates of point R?

R=(_,_)

Answer 1

R = (3, 14 )

Explanation:

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

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

calculate the midpoint of PR using this formula and equate x and y coordinates to the coordinates of the given midpoint

let coordinates of R be (x, y ) and P = (- 15, 4 ) , then

`(x-15)/(2)` = - 6 ( multiply both sides by 2 )

x - 15 = - 12 ( add 15 to both sides )

x = 3

and

`(y+4)/(2)` = 9 ( multiply both sides by 2 )

y + 4 = 18 ( subtract 4 from both sides )

y = 14

the coordinates R = (3, 14 )