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.

Explanation

i) Let AD be the median of the triangle ABC


Hence D is the midpoint of BC which can be found using the Mid Point formula.


`M = [(x_1 + x_2) / 2, (y_1 + y_2) /2]`


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