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Centroid of a Triangle

A 2,-3 and B ...

Question

A (2,-3) and B (-2,1) are vertices of $△ A B C$ . If the centroid of the triangle is on the line 2x+3y=1, then locus of vertex C is

3x+2y=5

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2x-3y=7

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2x+3y=9

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3x-2y= 4

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Solution

The correct option is D 2x+3y=9
Let $C (h, k)$
$C e n t r o i d x_{1} = h / 3 y_{1} = (- 2 + k) / 3$
$x_{1}, y_{1}$ lies on $2 x + 3 y = 1$
$\Rightarrow \frac{2 h}{3} - 2 + k = 1 \Rightarrow 2 h + 3 k = 9 2 x + 3 y + 9$

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