Question

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

• A. 4

Answer 1

The correct option is A 4
Points A(a, 3), B(2, 1) and C(5, a) are collinear. therefore, points A,B,C lie on the same line
$\therefore$ 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 $a=-1$
$\therefore$ poistive value of a is 4.