Q. The point moves such that the area of the triangle formed by it with the points (1, 5) and $(3,\ - 7)$ is 21 sq unit. The locus of the point is
A) $6x + y - 32$
B) $6x - y + 32 = 0$
C) $x + 6y - 32 = 0$
D) $6x - y - 32 = 0$
Explanation
(a)
Let the locus of point be $(x,\ y)$
Area of triangle with points $(x,\ y),\ (1,\ 5)$ and $(3,\ - 7)$ is 21 sq unit
$\therefore\frac{1}{2}\left| \begin{matrix}
x & y & 1 \\
1 & 5 & 1 \\
3 & - 7 & 1
\end{matrix} \right| = 21$
$\Rightarrow \frac{1}{2}\lbrack x(5 + 7) - y(1 - 3) + 1( - 7 - 15\rbrack = 21$
$\Rightarrow \frac{1}{2}\lbrack 12x + 2y - 22\rbrack = 21$
$\Rightarrow 6x + y - 32 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.