The number of the equilateral triangles in the plane have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.
What is an equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
There are 4 points, so there are C(4,2) = 4C2 = 6 pairs of points and since two equilateral triangles can be drawn having that pair of points as vertices, there are 12 equilateral triangles that can be drawn having two vertices in the set {(0,0), (0,1), (1,0), (1,1)}.
Therefore, the number of the equilateral triangles in the plane that have two vertices in the set {(0, 0), (0, 1), (1, 0), (1, 1)} will be 12.
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