Thread: Find the coordinates of the point of intersection of perpendicular bisectors

Hello, in a pre-calculus book I am given this problem:

Find the coordinates of the point of intersection of the perpendicular bisectors of the sides of a triangle whose vertices are located at (-a, 0), (b, c), and (a, 0).

The only apparent tools with which we are supposed to find the answer are the Pythagorean theorem, the distance formula, the midpoint formula, and the equation of a line.

I have tried this a couple of times but end up drowned in variables. Could anyone give me a hand?

Hello, Ragnarok!

Did you make a sketch?

Find the coordinates of the point of intersection of the perpendicular bisectors of the sides of a triangle
whose vertices are located at (-a, 0), (b, c), and (a, 0).

Code:

                |
                |    R
                |    * (b,c)
                | *   *
               *|      *
            *   |       *
     P   *      |        * Q
  - - * - - - - + - - - - * - -
   (-a,0)       |       (a,0)
                |

The perpendicular bisector of side is the y-axis, .[1]

The slope of side is
. . The perpendicular slope is
. . . . The midpoint of side is

The equation of the perpendicular bisector of side is:
. . .[2]

The intersection of [1] and [2] is: .