posted by Alex on .
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?
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