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) 1, 0 (C) 1, 2 (D)  1,-1/2

Tardigrade Admin · Accepted Answer

∵ Points (k,3),(2,k),(-k,3) are collinear. | beginmatrix k 3 1 2 k 1 -k 3 1 endmatrix |=0 ⇒ k(k-3)-3(2+k)+1(6+k2)=0 ⇒ k2-3k-6-3k+6+k2=0 ⇒ 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

1, 0

1, 2

$1, - 1/2$

0, 3

$∵$ Points $(k, 3), (2, k), (- k, 3)$ are collinear.
$∣ ∣ k 2 - k 3 k 3 111 ∣ ∣ = 0$
$\Rightarrow$ $k (k - 3) - 3 (2 + k) + 1 (6 + k^{2}) = 0$
$\Rightarrow$ $k^{2} - 3 k - 6 - 3 k + 6 + k^{2} = 0$
$\Rightarrow$ $2 k^{2} - 6 k = 0$
$\Rightarrow$ $k (k - 3) = 0$
$\Rightarrow$ $k = 0, 3$

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