Question

Value of p for which the points $(-5,1),(1,p)$ and $(4,-2)$ are collinear

• A. $0$
• B. $2$
• C. $-1$
• D. None of these

Answer 1

The correct option is C $-1$

Since the given points are collinear, they do not form a triangle, which means area of the triangle is zero.
Hence, substituting the points $(x_1,y_1)=(-5,1)$ ; $(x_2,y_2)=(1,p)$ and $(x_3,y_3)=(4,-2)$
In the area formula, we get
$\left|\frac{-5(p+2)+1(-2-1)+4(1-p)}{2}\right|=0$
$\Rightarrow -5p-10-3+4-4p=0$
$\Rightarrow 9p=-9$
$\Rightarrow p=-1$