Given the points `A(1, 2), B (8, 4), C(4, 10)`. Find the coordinates of the point `P` such that the triangle `PCB, PCA and PAB` have the same area in magnitude and sign.

Find the coordinates of the points which trisect the line segment A B , given that A(2,1,-3) and B(5,-8,3)

If A(1,p^(2)),B(0,1) and C(p,0) are the coordinates of three points then area of the triangle ABC is 1/(lamda)|p^(3)-p+1| . The value of lamda is

Prove that the points A(1, -3), B (-3, 0) and C(4, 1) are the vertices of an isosceles right- angled triangle. Find the area of the triangle.

The coordinates ofi as point P are (1,2,3). Find the coordinates for the seven points such that the absolute values of their coordinates are the same as those of coordinates of P.

A(4,\ 2),\ B(6,5) and C(1,\ 4) are the vertices of A B C . Find the coordinates of point P on A D such that A P : P D=2:1 .

Prove that the points A (1,-3) B (-3,0) and C(4,1) are the vertices of an isosceles right angle triangle. Find the area of the triangle.

A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle. Find the coordinates of the centroid G of the triangle.

Find the centroid of the triangle ABC whose vertices are A (9, 2), B (1, 10) and C (-7, -6) . Find the coordinates of the middle points of its sides and hence find the centroid of the triangle formed by joining these middle points. Do the two triangles have same centroid?

Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Delta A B C . (i) The median from A meets BC at D. Find the coordinates of the point D. (ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1 (iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.

The points A (x_(1),y_(1)), B (x_(2),y_(2)) and C (x_(3),y_(3)) are the vertices of triangle ABC. (i) The median from A Meets Bc at D. Find the coordinates of the points D. (ii) Find the coordinates of the point P on Ad such that AP : PD = 2 : 1 . (iii) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE=2 :1 and CR : RF =2 : 1 . What are the coordinates of the centroid of the triangle ABC?