Question

If points (p - 2, p - 4), (p, p + 1) and (p + 4, 16) are collinear then p = ?

• A. 4
• B. 5
• C. 6
• D. -2

Answer 1

Answer: (B)

5

The given points are collinear if and only if Area of triangle$=0$

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

where $x_1=p-2,y_1=p-4,x_2=p,y_2=p+1,x_3=p+4$ and $y_3=16$

$\Rightarrow \left|\begin{array}{ccc}p-2& p-4& 1\\ p& p+1& 1\\ p+4& 16& 1\end{array}\right|=0$

$\Rightarrow (p-2)(p+1-16)-(p-4)(p-p-4)+1(16p-(p+1)(p+4))=0$

$\Rightarrow (p-2)(p-15)+4(p-4)+(16p-(p+1)(p+4))=0$

$\Rightarrow p^2-17p+30+4p-16+16p-p^2-5p-4=0$

$\Rightarrow -2p+10=0$

$\Rightarrow 2p=10$

$\therefore p=5$