Question

The points $(1,1),(-5,5)$ and $(13,\lambda )$ lie on the same straight line, if $\lambda$ is equal to:

• A. 7
• B. $-7$
• C. $\pm 7$
• D. 0
• E. 14

Answer 1

Answer: (B)

Since the given points lies on a line $\left|\begin{array}{ccc}1& 1& 1\\ -5& 5& 1\\ 13& \lambda & 1\end{array}\right|=0$ $\Rightarrow$ $1(5-\lambda )-1(-5-13)+1(-5\lambda -65)=0$ $\Rightarrow$ $5-\lambda +18-5\lambda -65=0$ $\Rightarrow$ $-6\lambda =42$ $\Rightarrow$ $\lambda =-7$