Question

Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear.

• A. $a=-4$ or $a=1$
• B. $a=4$ or $a=-1$
• C. $a=3$ or $a=-2$
• D. $a=2$ or $a=-3$

Answer 1

The correct option is B

$a=4$ or $a=-1$

Points A(a, 3), B(2, 1) and C(5, a) are collinear.
$\therefore$ Slope of AB = Slope of BC
$\Rightarrow \frac{1-3}{2-a}=\frac{a-1}{5-2}$
$\Rightarrow \frac{-2}{2-a}=\frac{a-1}{3}$
$\Rightarrow \frac{2}{a-2}=\frac{a-1}{3}$
$\Rightarrow 6=a^2-3a+2$
$\Rightarrow a^2-3a-4=0$
$\Rightarrow (a-4)(a+1)=0$
Either $a-4=0$ or $a+1=0$
$\Rightarrow$ $a=4$ or $a=-1.$