Finding coordinates of one point of an equilateral triangle when other 2 points are given.

Dear Student

 

Let A(3,4) and B (-2,3) be the two given vertices and (x,y) be the third vertex

So

AC =BC =AB

 

or AC²=BC²=AB²

 

 (x-3)² + (y-4)² = (x+2)²+(y-3)² = 26

AC² =BC² gives

y =6-5x

Use this in

BC²= AB²

to get

x²+4x+4+9+25x²-30x=26

or 26 x²-26x-13=0

or 2x²-2x-1=0

so x =

Now find y = 6-5( )=