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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

(1,73)

(13,53)

(13,1)

(13,2)

Solution:

Correct option is B (13,2)
Let B(α,β) and C(γ,δ)
α+1/2 = -1; ⇒ α = -3
β+2/2 = 1 ⇒ β = 0
⇒B(-3,0)
Now γ+1/2 = 2 ⇒ γ = 3
δ+2/2 = 3 ⇒ δ = 4
⇒C(3,4)
⇒centroid of triangle is G(1/3, 2).