Question

If the points $(-1,3),(2,p)$ and $(5,-1)$ are collinear, the value of $p$ is

• A. $1$
• B. $-1$
• C. $0$
• D. $\sqrt{2}$

Answer 1

Answer: (A)

$1$

Let $A(-1,3)$, $B(2,p)$ and $C(5,-1)$ be the given points.

Three points are collinear if $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0$

Therefore, $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0\Rightarrow -1(p-(-1\left)\right)+2(-1-3)+5(3-p)=0\Rightarrow -1(p+1)+2(-4)+5(3-p)=0\Rightarrow -p-1-8+15-5p=0\Rightarrow -6p+6=0\Rightarrow -6p=-6\Rightarrow p=1$

Hence $p=1$