Mark the tick against the correct answer in the following: If the points $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear then the value of $k$ is A. 2 B. $-3$ C. 5 D. $-4$

Home » Mark the tick against the correct answer in the following: If the points and are collinear then the value of is A. 2 B. C. 5 D.

Mark the tick against the correct answer in the following: If the points $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear then the value of $k$ is
A. 2
B. $-3$
C. 5
D. $-4$

CBSE | Class 12 | Determinants | Maths | RS Aggarwal

Mark the tick against the correct answer in the following: If the points $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear then the value of $k$ is
A. 2
B. $-3$
C. 5
D. $-4$

Solution:

Option(C)
To find: Area of $A B C$
Given: $A(3,-2), B(k, 2)$ and $C(8,8)$
The formula used: $\Delta=\frac{1}{2}\left|\begin{array}{lll}x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1\end{array}\right|=0$
We have, $A(3,-2), B(k, 2)$ and $C(8,8)$
$\Delta=\frac{1}{2}\left|\begin{array}{ccc} 3 & -2 & 1 \\ k & 2 & 1 \\ 8 & 8 & 1 \end{array}\right|$
Expanding along $R_{1}$
$\begin{array}{l} \Rightarrow \frac{1}{2}[3\{(2)(1)-(8)(1)\}-(-2)\{(k)(1)-(8)(1)\}+1\{(k)(8)-(2)(8)\}]=0 \\ \Rightarrow \frac{1}{2}[3\{2-8\}+2\{k-8\}+1\{8 k-16\}]=0 \\ \Rightarrow-18+2 k-16+8 k-16=0 \end{array}$
$\begin{array}{l} \Rightarrow 10 \mathrm{k}-50=0 \\ \Rightarrow \mathrm{k}=5 \end{array}$