Find the coordinates of a point equidistant from two given points

Question

The Coordinates of two points are A(-2,6) and B(9,3). Find the coordinates of the point C on the x-axis such that AC = BC

Answer 1

A general approach:

Given two points $A$ and $B$, the line that is perpendicular to the segment $AB$ and goes through its midpoint is precisely the set of points that are equidistant from $A$ and $B$.

Answer 2

I agree with Andres C. that you have to find the equation of the perpendicular bisector of points A and B. And also with what Ross M. says that you must find out where this perpendicular bisector intersects with the x axis by substituting y=0.