Question

derive the coordinate of centroid

Answer 1

Step-by-step explanation:

A centroid divides the median in the ratio 2:1. Hence, since 'G' is the median so that AG/AD = 2/1. Since D is the midpoint of BC, coordinates of D are ((x2 + x3)/2, (y2 + y3)/2) By using the section formula, the coordinates of G are ([2(x2+x3)/2) +1× x1] / 2+1, ([2(y2+y3)/2) +1

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Answer 2

Answer:

Derivation of centroid formula

Sol: Let centroid of the triangle the coordinates of whose vertices are given by A(x1, y1), B(x2, y2) and C(x3, y3) respectively. A centroid divides the median in the ratio 2:1. Hence, since ‘G’ is the median so that  AG/AD = 2/1. Since D is the midpoint of BC, coordinates of D are ((x2 + x3)/2, (y2 + y3)/2) By using the section formula, the coordinates of G are ([2(x2+x3)/2) +1× x1] / 2+1, ([2(y2+y3)/2) +1.y1] / 2+1) ∴Coordinates of the centroid G are[ (x1+x2+x3) / 3, (y1+y2+y3 ) / 3].