Question

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

• A. A circle
• B. Any straight line
• C. A line parallel to L
• D. A line perpendicular to L

Answer 1

Answer: (C)

A line parallel to L

Assume that $(x,y)$ satisfy the given line.

Line $=9x+7y+4=0-\left(3\right)$

So, the centroid ( $h,k$ ) must be

$h=\frac{2+4+x}{3}$

$[$ formula $=\frac{x_1+x_2+x_3}{3}]$

$\Rightarrow x=3h-6-\left(1\right)$

and

$k=\frac{5-11+y}{3}$

$\Rightarrow y=3k+6-\left(2\right)$

Put (1) and (2) in (3)

$9(3n-6)+7(3k+6)+4=0$

$\Rightarrow 27h+21k-8=0$

$\Rightarrow y=\frac{8}{21}-\frac{9}{7}x$

So, slope $=m=-9/7$ (parallel)

The slope of given line is also $-9/7.$