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  4. If A(2, -3) and B(-2, 1) are two vertices of a triangle and third vertex moves on the line 2x + 3y = 9 , then the locus of the centroid of the triangle is :

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Q. If A(2, -3) and B(-2, 1) are two vertices of a triangle and third vertex moves on the line 2x + 3y = 9 , then the locus of the centroid of the triangle is :

AIEEEAIEEE 2011Straight Lines

Solution:

$\alpha = 3h$
$\beta - 2 = 3k$
$\beta = 3k +2$
third vertex on the line
$2x + 3y = 9$
$2\alpha + 3\beta= 9$
$2\left(3h\right) + 3\left(3k + 2\right) = 9$
$2h + 3k = 1$
$2x + 3y - 1 = 0$

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