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

1. AD is the median on BC. Find the coordinates of the point D.

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

3. Find the coordinates of points Q and R on medians BE and CF

4. Find the points which divide the line segment BE in the ratio 2 : 1 and also that divide the line segment CF in the ratio 2 : 1.

5. What do you observe?

Justify that the point that divides each median in the ratio 2 : 1 is the centriod of a triangle.


7.7 CENTROID OF A TRIANGLE

The centroid of a triangle is the point of concurrency of its medians.

Let A(x1 , y1 ), B(x2 , y2 ) and C(x3 , y3 ) be the vertices of the triangle ABC.

Let AD be the median bisecting its base. Then,

D = (x2 + x3/ 2 ,y2 + y3/ 2 ,)

Now the point G on AD which divides it internally in the ratio 2 : 1, is the centroid. If (x, y) are the coordinates of G, then




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