If Q is the midpoint of PR, find the coordinates of R if P(11, -2) and Q(4,3)

R = (- 3, 8 )

Step-by-step explanation:

Using the midpoint formula , equate the coordinates to the corresponding coordinates of Q.

let R = (x, y ) , then

(x + 11 ) = 4 ( multiply both sides by 2 )

x + 11 = 8 (subtract 11 from both sides )

x = - 3

(- 2 + y) = 3 ( multiply both sides by 2 )

- 2 + y = 6 ( add 2 to both sides )

y = 8

Thus

R = (- 3, 8 )

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.