0
$\begingroup$

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

  • 2
    Use the distance formula on a point $(c,0)$ ; solve for $c$.2010-11-24

2 Answers 2

3

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 $B$.

  • 0
    Correct, but then you have to find the intersection with the x axis.2010-11-24
  • 1
    @Hi Ross. That's correct. I think in general this is cleaner than playing with the distance formula.2010-11-24
  • 0
    Well, using the distance formula seems to require less computation in this case.2010-11-24
0

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.