A line segment has endpoints P(4, 0) and R (2, -4). The point Q is the midpoint of PR. What is an equation of a line perpendicular to PR and passing through Q?

Answer 1

Q is (3,-2) just average the x and y coordinates to get the midpoint

(4+2)/2 =6/2 =3, and (0-4)/2 = -4/2 =-2

(4,0) and (2,-4)

a line through them has slope = (0- -4)/(4-2) = 4/2 = 2

a perpendicular line has slope that's the negative inverse or -1/2

y=-x/2 + b, solve for b by plugging in the midpoint (3,-2)

-2 =-3/2 + b

b = -2 +3/2 = -1/2

y=-x/2 -1/2 or

2y=-x -1 or

x+2y = -1 is the perpendicular line through the midpoint