SOLUTION: How many equilateral triangles in the plane have two vertices in the set {(0,0), (0,1), (1,0), (1,1)}?

Algebra.Com
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
RELATED QUESTIONS

How many equilateral triangles in the plane have two vertices in the set {(0,0), (0,1),... (answered by KMST)
An equilateral triangle is one in which all three sides are of equal length. If two... (answered by mananth)
If two vertices of an equilateral triangle are (0, 4) and (0, 0), Find the third vertex.... (answered by Fombitz)
If two vertices of an equilateral triangle are (0,0) and (0,4), find the third vertex.... (answered by math_tutor2020,ikleyn)
How many points in a plane are in the locus of all points equidistant from two parallel... (answered by stanbon)
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars... (answered by CPhill)
A regular octahedron is made up of eight equilateral triangles, each with side length one (answered by ikleyn,greenestamps)
how many subsets does the set p= { -1, 0, 1, 2}... (answered by jim_thompson5910)
State the perimeter of each of the following triangles in simplest radical form, 1.... (answered by Alan3354)