Question

AD is the median of the triangle ABC and A=(1,3),D=(4,6).Find the centroid of triangle ABC​

Answer 1

Answer:

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Answer 2

The centroid of the triangle ABC is equal to (3,5).

The centroid of a triangle divides the median in the ratio 2:1.

Let the coordinates of the centroid be equal to (x,y).

The centroid will divided the line between A (1,3) and D(4,6) in the ratio 2:1.

Using the section formula to find the coordinates of the centroid -

x = (m1x2 + m2x1)/(m1+m2)

y = (m1y2 + m2y1)/(m1+m2)

Put the values x1 = 1 , x2 = 4 , y1 = 3 , y2 = 6 , m1 = 2 , m2 = 1 to get the coordinates of the centroid.

x = 8 + 1 / 3 = 3

y = 12 + 3 / 3 = 5