Question 970792
K is a midpoint.

The distance between M and K is
sqrt[ (xl-x2)^2 + (y1-y2)^2].  it can also be x2-x1 and y2-y1.  Because it can be squared, it can even be out of order, but I don't recommend doing that.

In any case the MK distance is sqrt [(5-x)^2 + (7-4)^2}= sqrt (25-10x+x^2 + 9}
The KN distance is sqrt[(x-4)^2+ (4-8)^2} =sqrt [(x^2-8x+16 +16)= sqrt(x^2 -8x +32)

These have to equal themselves, and we can remove the radicals.

x^2-10x +34=x^2 -8x +32

Subtract x^2 from both sides.

-10x +34 = -8x +32
-2x=-2 by adding 8x to both sides and subtracting 34 from both sides

x=1

Point is (1,4)

Check: MK is sqrt (16+9)   point KN is sqrt (9+16)

{{{ graph (300,300,-5,5,-2,9,-x+12)}}}

This shows the line extended equally in both directions.  Note where (1.4) would be relative to the ends of the line.