# Find the coordinates of a point equidistant from two given points

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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Use the distance formula on a point $(c,0)$ ; solve for $c$. –  Ｊ. Ｍ. Nov 24 '10 at 14:19
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## 2 Answers

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 $B$.

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Correct, but then you have to find the intersection with the x axis. –  Ross Millikan Nov 24 '10 at 16:02
@Hi Ross. That's correct. I think in general this is cleaner than playing with the distance formula. –  Andres Caicedo Nov 24 '10 at 16:05
Well, using the distance formula seems to require less computation in this case. –  Vlad Nov 24 '10 at 19:03
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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.

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