Question

If the points $(0,4),(4,0)$ and $(5,p)$ are collinear, then value of $p$ is

• A. $-1$
• B. $7$
• C. $6$
• D. $4$

Answer 1

The correct option is A $-1$

The given points are $A=(x_1,y_1)=(0,4),B=(x_1,y_1)=(4,0),C=(x_1,y_1)=(5,p)$.

They are collinear.

$\therefore ar\Delta ABC=0$

$\Rightarrow \frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|=0$

$\Rightarrow \left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|=0$

$\Rightarrow \left|\begin{array}{ccc}0& 4& 1\\ 4& 0& 1\\ 5& p& 1\end{array}\right|=0$

$\Rightarrow 0(0-p)+4(p-4)+5(4-0)=0$

$\Rightarrow p=-1$