Find the value of m if the perpendicular bisector of the line that passes through the point (6,8) and (m,2) has slope -2.

We'll remember the fact that the product of the values of
the slopes of 2 perpendicular lines is -1.

We know that the
slope of perpendicular bisector is -2.

-2*a = -1, a is the
slope

a = 1/2

The slope of
the line that passes through points  (6,8) and (m,2) is a =
1/2.

We'll write the formula of the
slope:

a = (2-8)/(m-6)

1/2 =
-6/(m-6)

m-6 = -12

m = -12 +
6

k = -6

The
value of the coordinate m is: m = -6.