Question

Consider a triangle ABC, whose vertices are $A(-2,1),B(1,3)$ and $C(x,y)$. If C is a moving point such that area of $\Delta$ABC is constant, then locus of C is?

• A. Straight line
• B. Circle
• C. Ray
• D. Parabola

Answer 1

The correct option is A Straight line

Area of $\Delta ABc$ is given by,

$K=\frac{1}{2}\left|\begin{array}{ccc}-2& 1& x\\ 1& 3& y\\ 1& 1& 1\end{array}\right|$

$k=\frac{1}{2}[-2(3-y)-1(1-y)+x(1-3\left)\right]$

$⟹2k=-6+2y-1+y-2x$

$⟹3y-2x=7+2k$

Hence the locus of $C$ is straight line.