What is the value of constant k if the perpendicular bisector of the segment with endpoints (k,0) and (4,6) has slope of -3?

The perpendicular bisector of the segment with endpoints
(k,0) and (4,6) has a slope -3.

This gives the slope of the
line segment with end points (k,0) and (4,6) as 1/3. We get this as the product of the
slope of perpendicular lines is -1.

The slope of the line
segment between (k,0) and (4,6) is

s = (6 - 0)/(4 - k) =
1/3

=> 6 / (4 - k) =
1/3

=> 4 - k =
18

=> k = 4 -
18

=> k =
-14

The required value is k =
-14.