(i) The median from A meets BC at D. Find the coordinates of point D.

(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.

Solution:

(i) D’s coordinates can be computed using the formula below:

Coordinates of D = ( (6+1)/2, (5+4)/2 ) = (7/2, 9/2)

As a result, D is (7/2, 9/2)

(ii) P’s coordinates can be computed using the formula below:

Coordinates of P = ( [2(7/2) + 1(4)]/(2 + 1), [2(9/2) + 1(2)]/(2 + 1) ) = (11/3, 11/3)

As a result, P is (11/3, 11/3)