Question

Let A(2, - 3) and B(-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1 then the locus of the vertex C is the line

• A. 3x - 2y = 3
• B.
• C. 3x + 2y = 5
• D. 2x + 3y = 9

Answer 1

The correct option is D

2x + 3y = 9

Let the third vertex be $(x_1,y_1)$ then

Centroid (G) = $(\frac{x_1+2-2}{3},\frac{y_1-3+1}{3})$

i.e., G$(\frac{x_1}{3},\frac{y_1-2}{3})$

Given, centroid of triangle moves on the line

2x + 3y = 1

$\therefore$ 2$\left(\frac{x_1}{3}\right)+3\left(\frac{y_1-2}{3}\right)$ = 1 i.e., $2x_1+3y_1=9$ Locus of $(x_1,y_1)$ is 2x + 3y = 9