If the coordinates of the vertices of a triangle ABC be (3,0), (0,6)and (6,9)and if D and E respectively divide `overline(AB) and overline(AC)` internally in the ratio 1:2 , then show that the area of `DeltaABC=9`x the area of `DeltaADE`.

If the coordinates of the vertices of triangle A B C are (-1,6),(-3,-9) and (5,-8) , respectively, then find the equation of the median through Cdot

If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) , respectively, then find angleABC .

Coordinates of the vertices A,B,C of a triangle ABC are (m+3,m),(m,m-2)and (m+2,m+2) respectively Show that the area of the triangle ABC is independent of m .

Find the coordinates of centroid of the triangle with vertices: (1, -1), (0, 6) and (-3, 0)

The coordinates of the vertices A, B and C of a triangle ABC are (0,5), (-1,-2) and (11,7) respectively . Find the coordinates of the foot of the perpendicular from B on AC.

Find the area of the triangle vertices are (0, 0), (3, 0) and (0, 2)

Find the coordinates of centroid of the triangle with vertices: (6, 2), (0, 0) and (4, -7)

The coordinates of the points A,B,C,D are (0,-1),(-1,2),(15,2) and (4,-5) respectively . Find the ratio in which overline(AC) divides overline(BD) .

The vertices of a triangle ABC are (2,-5) , (1 ,-2) and (4,7) respectively . Find the coordinates of the point where the internal bisector of angleABC cuts AC .

Let us consider one vertex and one side through the vertex along x -axis of a triangle . Now the coordinates of the vertices B,C and A of any triangle ABC (0,0) ,(a,0) and (h,k) respectively should be taken . If in triangle ABC , AC =3 ,BC=4 and median AD is perpendicular with median BE , then the area of DeltaABC is -