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If the vertices of a traingle have integral coordinates, prove that the triangle cannot be equilateral.

Solve it and what is integral coordinates?

Here is the solution of your asked query:

Let us take the vertices of the triangle as , where all these coordinates are integers.

∴ Area of the triangle =

Since all the coordinates are integers, therefore, the area will be rational.

Let us assume that the triangle is equilateral, with length of its each side being *s*.

∴ Area of the triangle =

which is an irrational value.

Hence, our assumption that the area is rational, is wrong.

Thus,** the triangle with integral coordinates can not be an equilateral triangle.**

Integral coordinates are coordinates that are whole numbers. Integral coordinates cannot be fractional or have decimals.

Regards

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