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

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

Tardigrade Admin · Accepted Answer

Let points A(k, 3), B(2, k) and C(- k, 3) are collinear. Slope of AB = Slope of BC ⇒ (k-3/2-k)=(3-k/-k-2) ⇒ -k2+k+6=k2-5k+6 ⇒ 2k2-6k=0 ⇒ k(k - 3) = 0 ⇒ k=0, 3

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

$2$ , $3$

$0$ , $3$

$1$ , $0$

$1$ , $2$

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

Q. If the points (k,3), (2,k), (−k,3) are collinear, then the values of k are

2, 3

0, 3

1, 0

1, 2