Question

Find the value of 'a' for which the following points A(a, 6), B(4, 2) and C(10, a) are collinear.
$\left[3Marks\right]$

Answer 1

Points A(a, 6), B(4, 2) and C(10, a) are collinear.
$\therefore$ Slope of AB = Slope of BC
$\left[1Mark\right]$

$\Rightarrow \frac{2-6}{4-a}=\frac{a-2}{10-4}$

$\Rightarrow \frac{-4}{4-a}=\frac{a-2}{6}$

$\Rightarrow \frac{4}{a-4}=\frac{a-2}{6}$
$\left[1Mark\right]$

$\Rightarrow 24=a^2-6a+8$
$\Rightarrow a^2-6a-16=0$
$\Rightarrow (a-8)(a+2)=0$
Either $a-8=0$ or $a+2=0$
$\Rightarrow$ $a=8$ or $a=-2.$
$\left[1Mark\right]$