SOLUTION: If (-2,0) and (2,0) are two vertices of an equilateral TRIANGLE, find the possible location of the 3rd vertex

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Question 1003745: If (-2,0) and (2,0) are two vertices of an equilateral TRIANGLE, find the possible location of the 3rd vertex
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
Unknown point (x,y),

sqrt%28%28x%2B2%29%5E2%2By%5E2%29=4
and
sqrt%28%28x-2%29%5E2%2By%5E2%29=4

Can you work with those two equations, and find the common points, their intersection (either or both of them)?

Start with the first equation, and solve y^2 in terms of ....
find that y%5E2=16-%28x%2B2%29%5E2.
Substitute this into the other equation.
%28x-2%29%5E2%2By%5E2=16
%28x-2%29%5E2%2B%2816-%28x%2B2%29%5E2%29=16
and a few more steps to find
highlight%28x=0%29.

Go back to either equation of the system, use this found x=0, and solve for y.

You should find two possible y values. Not surprising that the two points will be on the vertical y-axis for x=0.