# 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?

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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.**

We'll recall 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 -3.

-3*m = -1

The slope of the segment whose endpoints are (k,0) and (4,6) is m = 1/3.

We'll write the formula of the slope:

m = (6-0)/(4-k)

1/3 = 6/(4-k)

4-k = 18

k = -18 + 4

k = -14

**The value of the constant k is k = -14.**