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  4. The points (1,1),(-5,5) and (13,λ ) lie on the same straight line, if λ is equal to:

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

KEAMKEAM 2003

Solution:

Since the given points lies on a line $ \left| \begin{matrix} 1 & 1 & 1 \\ -5 & 5 & 1 \\ 13 & \lambda & 1 \\ \end{matrix} \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 $