Question

find

the centroid of triangleABC if
A(2,3) B (4,5) c) (0,0)​

Answer 1

Answer:

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

Let D be the midpoint of side BC.

Since, the coordinates of B (x2, y2) and C (x3, y3), the coordinate of the point D are (x2+x32, y2+y32).

Let G(x, y) be the centroid of the triangle ABC.

Then, from the geometry, G is on the median AD and it divides AD in the ratio 2 : 1, that is AG : GD = 2 : 1.

Therefore, x = {2⋅(x2+x3)2+1⋅x12+1} = x1+x2+x33

y = {2⋅(y2+y3)2+1⋅y12+1} = y1+y2+y33

Therefore, the coordinate of the G are (x1+x2+x33, y1+y2+y33)

Hence, the centroid of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) has the coordinates (x1+x2+x33, y1+y2+y33).

Note: The centroid of a triangle divides each median in the ratio 2 : 1 (vertex to base).

Answer 2

Answer:

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