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?
Re: Find the coordinates of the point of intersection of perpendicular bisectors
Hello, Ragnarok!
Did you make a sketch?
Quote:
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:
. .  \quad\Rightarrow\quad y \:=\:\tfrac{a-b}{c}x + \tfrac{b^2+c^2-a^2}{2c})
.[2]
The intersection of [1] and [2] is: . )
