Find the value of so that the points (1, - 5), (-4, 5) and ( ,7) … - Vidyadip

Question

Find the value of $\lambda$ so that the points $(1, - 5), (-4, 5)$ and $(\lambda,7)$ are collinear.

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Answer

If the points are collinear, then the area of the triangle must be zero.
Hence,
$\begin{vmatrix}1&-5&1\\-4&5&1\\\lambda&7&1\end{vmatrix}=0$
Expanding along $R_1$
$1(-2)+5(-4-\lambda)+1(-28-5\lambda)=0$
$-2-20-5\lambda-28-5\lambda=0$
$-50-10\lambda=0$
$\lambda=5$
Hence, $\lambda=5$

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