Coordinate Geometry

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ∆ ABC.

(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 are the coordinates of the centroid of the triangle ABC?