Prove that the coordinates of the vertices of an equilateral triangle can not all be rational.

Prove that the co-ordinates of the vertices of an equilateral triangle can not be rational.

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Find the coordinates of the vertices of an equilateral triangle of side 2a as shown in Figure.

Find the coordinates of the vertices of an equilateral triangle of side 2 a as shown in Figure.

If the coordinates of two vertices of an equilateral triangle are (2,4) and (2,6), then the coordinates of its third vertex are

Prove that the medians of an equilateral triangle are equal.

Prove that the medians of an equilateral triangle are equal.

Prove that the medians of an equilateral triangle are equal.

Prove that the medians of an equilateral triangle are equal.