A triangle has a vertex at ( 1 , 2 ) and the mid points of the two sides through it are ( - 1 , 1 ) and ( 2 , 3 ) . Then the centroid of this triangle is:

Question

A triangle has a vertex at ( 1 , 2 ) and the mid points of the two sides through it are ( - 1 , 1 ) and ( 2 , 3 ) . Then the centroid of this triangle is:, 1 3 , 1, 1 , 7 3, 1 3 , 2, 1 3 , 5 3

MARKS App · Accepted Answer

Let co-ordinates of B = x 1 , y 1 ∴ x 1 + 1 2 = - 1 & y 1 + 2 2 = 1 ⇒ x 1 = - 3 , y 1 = 0 ∴ B = ( - 3 , 0 ) Let co-ordinates of C = x 2 , y 2 ∴ x 2 + 1 2 = 2 & y 2 + 2 2 = 3 ∴ C = 3 , 4 Let centroid G = h , k h = 1 + x 1 + x 2 3 = 1 - 3 + 3 3 = 1 3 k = 2 + y 1 + y 2 3 = 2 + 0 + 4 3 = 2 ∴ Centroid, G = 1 3 , 2

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