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(x1+x2+x3)/3, (y1+y2+y3)/3
Hope my answer helps
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].
Hope my answer helps
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].
Anonymous:
but this is the direct answer
I need step by step
Ok
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].
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].
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