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Let A(4,2) ,B (6,5) andC(1,4) be the vertices of DeltaABC . (i) The medium fromA meetsBC at D . Find the coordinates of the point D. (ii) Find the coordinatesof the point P on AD such that AP:PD = 2:1 (iii) Find the coordinates of points Q and R onmedians BE and CF respectively such that BQ:QE = 2:1 and CR:RF = 2:1 . (iv) What do you observe? [ Note : The point which is commonto all the three medians is called the centroidand this pointdivides each medianin the ratio 2:1] (v) If A(x_(1),y_(1)),B(x_(2),y_(2))and C(x_(3),y_(3))are the vertices of triangleABC , find the coordinates of the centroid of the triangle . |
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