`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` .

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. The median from A meets BC in D Find the coordinates of the point D

If A(4, 2), B(6, 5) and C(1, 4) be the vertices of Delta ABC and AD is a median, then the coordinates of D are

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.

7. Let A (4, 2) B(6.,5) and C(1.,4). be the vertices of DeltaABC. (1) The median from A meets BC at D. Find the coordinates of the point D. (2) the coordinates of the point P on AD such that AP: PD= 2:1. (3) 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. (4) what do yo observe?

A (4,8), B(5,5), C(2,4) and D (1,7) are the vertices of the parallelogram . Find the coordinates of the point of intersection of its diagonals .

If A(-2,-1),B(p,0),C(4,q) and D(1,2) are the vertices of a parallelogram, find the values of p and q.

A(4,3),B(6,5)and C(5,-2) are the vertices of a DeltaABC, if P is a point on BC such that BP:PC =2:3. Find the co-ordinates of P and then prove then ar (DeltaABP):ar(DeltaACP)=2:3.

The vertices f the triangle are A(5,4,6), B(1,-1,3)n a d C(4,3,2)dot The internal bisector of angle A meets BC at D. Find the coordinates of D and the length AD.