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...

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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.**