Question 981273: How many equilateral triangles in the plane have two vertices in the set {(0,0), (0,1), (1,0), (1,1)}?
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Given two points, two equilateral triangles can be
drawn having those two points as vertices.
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)}.
Answer: 12
Here are the 8 equilateral triangles using the sides of the square as vertices:
Here are the 4 equilateral triangles using the 2 diagonals
of the square as a side.
Here are all 12, all black:
Edwin
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website! Question 981273
Given two points, two equilateral triangles can be
drawn having those two points as vertices.
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)}.
Answer: 12
Here are the 8 equilateral triangles using the sides of the square as vertices:
Here are the 4 equilateral triangles using the 2 diagonals
of the square as a side.
Here are all 12, all black:
Edwin
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