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in Coordinate Geometry by (28.9k points)
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If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

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We know that centroid of ∆DEF will be the same that of ∆ABC as ∆DEF is formed by midpoints of ∆ABC.

∴ We know that centroid of a triangle for (x1 , y1), (x2 , y2) and (x3 , y3) is

G(x,y) = \((\frac{x_1+x_2+x_3}3,\frac{y_1+y_2+y_3}3)\)

∴ G(x, y) = \((\frac{4+4-2}3,\frac{5-3+3}3)\)

∴ G(x, y) = ( 2, \(\frac{5}2\))

Hence the centroid is ( 2, \(\frac{5}2\))

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