SOLUTION: Please help me solve this :) M(5,7), K(x,4), N(4,8) are given. If K is at the same distance from the ponts M and N, then find x

Question 970792: Please help me solve this :)

M(5,7), K(x,4), N(4,8) are given. If K is at the same distance from the ponts M and N, then find x
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
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)

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