Question

the points (0,0) and (-2,2) are two vertices of an equilateral triangle. Which of the following could be the coordinates of the third vertex?
A. (-2,0)
B. (-0.73, 2.73)
C. (-0.73, 0.73)
D. (0,2)
E. (0.73, 2.73)

Answer 1

equilateral triangle is one where all points have the same distance to each other: https://upload.wikimedia.org/wikipedia/commons/thumb/9/96/Triangle.Equilateral.svg/220px-Triangle.Equilateral.svg.png

Answer 2

the line 0,0 <-> -2,2 is already fixed. Pythagoras: \[2^{2}+2^{2} = x^2\]
\[4+4 = x^2\]
\[\sqrt{8} = x =2.82 \]

Answer 3

we need a point where both lines=2.82 in length:
0,0 <-> X =2.82 AND
-2,2 <-> X=2.82

Answer 4

we can try with the values one should work.....

Answer 5

I would make a quick sketch (plot the points)
and see which one looks reasonable

Answer 6

yes

Answer 7

and use the fact that the length of all sides is about 2.8 (as posted by phanta_seea) to rule out some obviously wrong points