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 :

Question

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 : (A) x - y = 1 (B) 2x + 3y = 1 (C) 2x + 3y = 3 (D) 2x - 3y = 1

Tardigrade Admin · Accepted Answer

α = 3h β - 2 = 3k β = 3k +2 third vertex on the line 2x + 3y = 9 2α + 3β= 9 2(3h) + 3(3k + 2) = 9 2h + 3k = 1 2x + 3y - 1 = 0

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 :

x - y = 1

2x + 3y = 1

2x + 3y = 3

2x - 3y = 1

$α = 3 h$
$β - 2 = 3 k$
$β = 3 k + 2$
third vertex on the line
$2 x + 3 y = 9$
$2 α + 3 β = 9$
$2 (3 h) + 3 (3 k + 2) = 9$
$2 h + 3 k = 1$
$2 x + 3 y - 1 = 0$

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 :

x - y = 1

2x + 3y = 1

2x + 3y = 3

2x - 3y = 1

α=3h β−2=3k β=3k+2 third vertex on the line 2x+3y=9 2α+3β=9 2(3h)+3(3k+2)=9 2h+3k=1 2x+3y−1=0

$α = 3 h$
$β - 2 = 3 k$
$β = 3 k + 2$
third vertex on the line
$2 x + 3 y = 9$
$2 α + 3 β = 9$
$2 (3 h) + 3 (3 k + 2) = 9$
$2 h + 3 k = 1$
$2 x + 3 y - 1 = 0$