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 :

(\frac{1}{3}, 1)

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(\frac{1}{3}, 2)

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(1, \frac{7}{3})

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(\frac{1}{3}, \frac{5}{3})

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Solution

The correct option is B $(\frac{1}{3}, 2)$

As $E$ is the midpoint of $A B$ , we get
$\frac{x_{2} + 1}{2} = - 1, \frac{y_{2} + 2}{2} = 1 \Rightarrow x_{2} = - 3, y_{2} = 0$
Point $B$ is $(- 3, 0)$

Similarly, point $C$ is $(3, 4)$
So, centroid of the triangle is
$(\frac{1 - 3 + 3}{3}, \frac{2 + 0 + 4}{3}) = (\frac{1}{3}, 2)$

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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 :