ConceptArea of a Triangle

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#### Question

Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of ΔABC.

(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

(iii) Find the coordinates of point 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 ΔABC, find the coordinates of the centroid of the triangle.

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#### Reference Material

Solution for concept: Area of a Triangle. For the course CBSE