SOLUTION: Find the third vertex C(x,y) of an equilateral triangle if the other vertices are A(-4,-1) and B (4,3)

Algebra ->  Triangles -> SOLUTION: Find the third vertex C(x,y) of an equilateral triangle if the other vertices are A(-4,-1) and B (4,3)      Log On


   

Question 1107134: Find the third vertex C(x,y) of an equilateral triangle if the other vertices are A(-4,-1) and B (4,3)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Each triangle side is 2sqrt%2810%29, found using distance-formula. This means AB=BC=CA=2%2Asqrt%2810%29.

Slope of AB is 1%2F2, and then slope of the line perpendicular to AB and containing point C must be -2. Also This perpendicular bisector line must contain midpoint of AB, which is (using Midpoint formula), (0,1).
This means, line containing point C is y=-2x%2B1.

sqrt%28%28-4-x%29%5E2%2B%28-1-%282x%2B1%29%29%5E2%29=2%2Asqrt%2810%29
and
sqrt%28%284-x%29%5E2%2B%283-%282x%2B1%29%29%5E2%29=2%2Asqrt%2810%29
.
.

Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
This problem is solved in two steps. 

 
    Step 1.   Make a sketch on a squared paper.


    Step 2.  Look in it and think where to place the third vertex.


Your goal is to put the third vertex in a way to get  CONGRUENT  right  angled  TRIANGLES  using squares on the paper.

The method is the combination of   a)  "trial and guess",   b)  looking;   and   c)  thinking. 


    The problem CAN BE SOLVED  and  MUST BE SOLVED  without any calculations . . . 

    Without any equations . . . Without any systems of equations . . . 

    Without any square roots . . .