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  4. If the area of the triangle with vertices (2,5),(7, k) and (3, 1) is 10 , then find the value of k.

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Q. If the area of the triangle with vertices $(2,5),(7, k)$ and $(3, 1)$ is $10$ , then find the value of $k$.

Gujarat CETGujarat CET 2017

Solution:

$10=\frac{1}{2} \begin{vmatrix}2 & 5 \\ 7 & k \\ 3 & 1 \\ 2 & 5\end{vmatrix}$
$k=5$ or $-35$