tricks-how to find vertices of a triangle when it's mid-points are given - Coordinate geometry

find the slope of a line when two points having coordinates are given?

The coordinates of the vertices of a triangle are (3, 1), (2, 3) and (-2, 2). Find the coordinates of the centroid of the triangle ABC :

The coordinates of the vertices of a triangles are (3,1) , (2,3) and (-2,2) . Find the coordinates of the centroid of the triangle ABC :

If the coordinates of vertices of a triangle is always rational then the triangle cannot be

If (-4,3) and (4,3) are two vertices of an equilateral triangle, then find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

If the points (1,-1),(2,-1) and (4,-3) are the mid points of the sides of a triangle then write the coordinates of its centroid.

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 third vertex of a triangle, if centroid of the triangle is (3,-5) and two of its vertices are (4,-8) and (3,6).