First slide

Cartesian plane

Question

If a vertex of a triangle is $(1, 1)$ and the mid points of two sides through this vertex are $(- 1, 2)$ and $(3, 2)$ , then centroid of the triangle is

Easy

A

$(1, 7 / 3)$
B

$(1 / 3, 7 / 3)$
C

$(- 1, 7 / 3)$
D

$(- 1 / 3, 7 / 3)$

Solution

Let $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ be the other two vertices of the triangle, then $\frac{x_{1} + 1}{2} = - 1, \frac{y_{1} + 1}{2} = 2$
$\Rightarrow (x_{1}, y_{1}) = (- 3, 3);$ similarly $(x_{2}, y_{2}) = (5, 3)$
centroid of the triangle is $(\frac{1 - 3 + 5}{3}, \frac{1 + 3 + 3}{3}) = (1, 7 / 3)$

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