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

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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)   (Show Source): You can put this solution on YOUR website!
Each triangle side is , found using distance-formula. This means .

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


and

.
.
Answer by ikleyn(52795)   (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 . . .


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