Question

$A(2,-5)$ and $B(-7,6)$ are two vertices of a triangle. Find the equation of the locus of the third vertex, $C$ if the centroid of the triangle lies on the locus $3x-4y+11=0$

• A. $3x+4y+14=0$
• B. $3x-4y+14=0$
• C. $3x-4y-14=0$
• D. None of these

Answer 1

The correct option is B $3x-4y+14=0$

REF.Image

Centroid $\equiv \frac{h-7+2}{3},\frac{k-5+6}{3}$

$\equiv \frac{h-5}{3},\frac{k+1}{3}$

Centroid lies on $3x-4y+11=0$

$3\left(\frac{h-5}{3}\right)-4\left(\frac{k+1}{3}\right)+11=0$

$3(h-5)-4(k+1)+33=0$

$3h-15-4k-4+33=0$

$3h-4k+14=0$

$3x-4y+14=0$