Points `A(x_1,y_1)`, `B(x_2, y_2)` and `C(x_3, y_3)` are the vertices of `triangle ABC`.
Find the cooridnates of the point P on AD such that AP:PD = 2:1.

A(4,2), B(6,5) and C(1,4) are the vertices of triangle ABC Find coordinates of points P on AD such that AP : PD= 2: 1 .

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

If A(x_(1),y_(1)),B(x_(2),y_(2)) and C(x_(3),y_(3)) are the vertices of a triangle then excentre with respect to B is

The points A (x_(1),y_(1)), B (x_(2),y_(2)) and C (x_(3),y_(3)) are the vertices of Delta ABC . What are coordinate of the centroid of the triangle ABC ?

If A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) are the vertices of the triangle then show that:'

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?

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. (iv) What do you observe? (v) If A(x_(1),y_(1)), B(x_(2),y_(2)) and C(x_(3),y_(3)) are the vertices of ∆ ABC, find the coordinates of the centroid of the triangle.

If A(x_1, y_1), B (x_2, y_2) and C (x_3, y_3) are the vertices of a DeltaABC and (x, y) be a point on the internal bisector of angle A , then prove that : b|(x,y,1),(x_1, y_1, 1), (x_2, y_2, 1)|+c|(x, y,1), (x_1, y_1, 1), (x_3, y_3, 1)|=0 where AC = b and AB=c .

If the points (x_1 , y_1), (x_2, y_2) and (x_3, y_3) be the three consecutive vertices of a parallelogram, find the coordinates of the fourth vertex.