Question

If the points $(k, 3)$, $(2, k)$, $(- k, 3)$ are collinear, then the values of $k$ are

• A. $2$, $3$
• B. $0$, $3$
• C. $1$, $0$
• D. $1$, $2$

Answer 1

Answer: (B)

Let points $A(k, 3)$, $B(2, k)$ and $C(- k, 3)$ are collinear.
Slope of $AB =$ Slope of $BC$
$\Rightarrow \frac{k-3}{2-k}=\frac{3-k}{-k-2}$
$\Rightarrow -k^{2}+k+6=k^{2}-5k+6$
$\Rightarrow 2k^{2}-6k=0$
$\Rightarrow k\left(k - 3\right) = 0$
$\Rightarrow k=0$, $3$