What is the $x$-coordinate of the point on the $x$-axis that is equidistant from points $A( -2, 0)$ and $B(0,4)$?
Let the point we are seeking be (x , 0)
Simplifying from the distance formula, we have
(-2 - x)^2 = x^2 + 4^2
x^2 + 4x + 4 = x^2 + 16
4x = 12
x = 3
Let the point on the x-axis be (x,0). Since this point is equidistant from A and B, we have
[\sqrt{(x + 2)^2 + 0^2} = \sqrt{(x - 0)^2 + 4^2}]or (x+2)2=x2+16. Solving, we find x=−1.
+82 
