Posted by **Alex** on Monday, August 13, 2012 at 1:00pm.

Find k, given that (2,k) is equidistant from (3,7) and (9,1).

The answer is : k=0

How do I solve this problem?

- Algebra -
**Steve**, Monday, August 13, 2012 at 3:21pm
The slope of the line segment joining (3,7) and (9,1) is -6/6 = -1.

Any point equidistant from those two points will lie on the perpendicular bisector of that line segment.

So, we want the line with slope=1, through (6,4), the midpoint of the segment.

y-4 = 1(x-6)

Now, we plug in (2,k) to get

k-4 = 2-6

k = 0

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