The line represented by the equation y = - 2 x + 6 is

(-1,-2) If y= -2x + 6 is the perpendicular bisector of the segment AB, then the line containing segment AB must have a slop of 0.5 (the negative inverse of -2)

Question: - Why is the negative inverse of -2 0.5? I have it in my head that it is because opposite of 2/1 is 1/2 which is 0.5?.

Therefore you can represent this line with the equation y = 0.5x + b. Substitute the coordinates (7,2) into the equation to find the value of b.

2 = 0.5(7) + b
b = -1.5

Question: - Why does this equal -1.5? 0.5 x 7 = 3.5 / 2 = 1.75 ?

The line containing AB is y = 0.5 x - 1.5

Find the point at which the perpendicular bisector intersect AB by setting the two equations y = -x + 6 and y = 0.5x - 1.5x equal to each other.

-2x + 6 = 0.5x - 1.5
2.5 x = 7.5
x = 3, y = 0

The two lines intersect at (3,0) which is midpoint of AB.

X Y
A 7 2
MID 3 0
B -1 -2