Let A(4,2) B(6,5) and C(1,4)be the vertices of triangle. What do you observe? Justify that the point that divides each median in the ratio 2 : 1 is the centriod of a triangle.

A (2, 5), B (-1, 3) and C (5, -1) are the vertices of a triangle. The image of the point (1,2) with respect to the median through A is

If the points (3,-4) (1,6) and (-2,3) are the vertices of a triangle ,find its area.

Let A(0,beta), B(-2,0) and C(1,1) be the vertices of a triangle. Then Angle A of the triangle ABC will be obtuse if beta lies in

ABC is a triangle with vertices A(-1,4), B(6,-2), and C(-2, 4). D, E and F are the points which divide each AB, BC, and CA respectively in the ratio 3:1 internally. Then the centroid of the triangle DEF is

If A(1,-1), B(0,4), C(-5,3) are vertices of a triangle, then find the slope of each side.

Show that the points A(4, 7 ) B (8,4) and C(7,11) are the vertices of a right angled triangle.

Show that the points A (1,1,1), B (1,2,3) and C (2,-1,1) are vertices of an isosceles triangle.

Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of the triangle is the origin, find the coordinates of the third point.

The vertices of a triangle are A(-1, 3), B(1, -1) and C(5, 1) . Find the length of the median through the vertex C.