If the coordinates of the vertices of a triangle are rational numbers, then which of the following points of the triangle will always have rational coordinates

If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.

The coordinates of two vertices of a triangle are (-2,3) and (5,-1) . If the orthocentre of the triangle is at the origin , find the coordinates of its third vertex.

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

The coordinates of the vertices of a triangle are (4,-3) , (-5,2) and (x,y). If the centre of gravity of the triangle is at the origin then find x,y.

Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

The coordinates of the mid -point of the sides of a triangle are (0,1) (1,1)and (1,0),find the coordinates of the triangle.

Which of the following number(s) is/are rational?

If the midpoints of the sides of a triangle are (2,1),(-1,-3),a n d(4,5), then find the coordinates of its vertices.

The coordinates of the vertex A of the triangle ABC are (7,-4) . If the coordinates of the centroid of the triangle be (1,2) , find the coordinates of the mid - point of the side overline(BC) .

Find the coordinates of the vertices of a triangle of which D (2, -1), E (-1, 4) and F(-2, 2) are the mid-points of its sides.