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
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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 $B$.
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.