`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 A B C . Find the coordinates of the points Q and R on medians B E and C F respectively such that B Q : Q E=2:1 and C R : R F=2:1 . What do you observe?

A(4,\ 2),\ B(6,5) and C(1,\ 4) are the vertices of triangle A B C . The median from A meets B C in D . Find the coordinates of the point D .

If A(1,\ 2),\ \ B(4,\ 3) and C(6,\ 6) are the three vertices of a parallelogram A B C D , find the coordinates of fourth vertex D .

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.

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 points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices of a parallelogram ABCD. Find the vector equations of side AB and BC and also find the coordinates of point D .

The points A(4, 5, 10), B(2, 3, 4) and C (1, 2,-1) are three vertices of a parallelogram ABCD. Find the vector equations of the sides AB and BC and also find the coordinates of point D.

The points A(4, 5, 10), B(2, 3, 4) and C (1, 2,-1) are three vertices of a parallelogram ABCD. Find the vector equations of the sides AB and BC and also find the coordinates of point D.

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.

If A and B are (1,\ 4) and (5,\ 2) respectively, find the coordinates of P when A P//B P=3//4 .