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

For 25 points. If correct with work, will mark Brainliest. You can show an image for work.

The coordinate of points given are:

A(-1,-1)

B(4, 0)

C (0,4 )

For ABC to be isosceles , then AB must be equal to BC or AB = AC

The next thing to do is to find the value of AB , BC and AC using the formula for finding distance between two points which is given by:

D =

Calculating AB first , we have

=

=

Therefore:

AB =

Calculating BC , we have :

D =

D =

D =

Therefore :

BC =

Calculating AC , we have :

D =

D =

D =

Therefore :

AC =

Since AB = AC  BC then we can conclude that the triangle ABC is isosceles but not equilateral triangle

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step-by-step explanation: