Question

If the vertices A & B of a triangle ABC are given by (2,5) and (4, –11) respectively. And C moves along the line 9x + 7y + 4=0 then locus of centroid of $\Delta$ ABC is

• A. circle
• B. parallel to given line
• C. parabola
• D. perpendicular to given line

Answer 1

The correct option is B parallel to given line

Let $C(\alpha ,\beta )$ be the third vertex and let the coordinates of the centroid of $\Delta$ ABC is G (h, k). Then
$H=\frac{2+4+\alpha }{3}andk=\frac{5-11+\beta }{3}$

$\Rightarrow 6+\alpha =3hand-6+\beta =3k$
$\Rightarrow \alpha =3h–6and\beta =3k+6$
Since, $C(\alpha ,\beta )$ lies on the line
9x + 7y +4 = 0
$\therefore 9\alpha +7\beta +4=0$
$\Rightarrow$9(3h−6) + 7(3k+6) + 4 = 0
$\Rightarrow$ 27h – 54 + 21k + 42 + 4 = 0
$\Rightarrow$ 27h + 21k – 8 = 0
$\Rightarrow$ 3(9h + 7k) – 8 = 0
Hence, the locus of (h, k) is $9x+7y=\frac{8}{3}$ which is parallel to L.
Hence, (b) is the correct answer.