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  4. The area of triangle with vertices (K, 0),(4,0) , (0, 2) is 4 square units, then value of K is

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Q. The area of triangle with vertices $(K, 0),(4,0) , (0, 2)$ is $4$ square units, then value of $K$ is

KCETKCET 2017Determinants

Solution:

Let $A(K, 0), B(4,0), C(0,2)$
Now, we have
ar $(\Delta \,A B C)=4$
$ \therefore \frac{1}{2}|K(0-2)+4(2-0)+0(0-0)|=4 $
$ \Rightarrow \, \frac{1}{2}|-2 K+8|=4 $
$ \Rightarrow \, |-2 K+8|=8$
$ \Rightarrow -2 K+8=\pm 8$
$\Rightarrow -2 K=\pm 8-8$
$ \Rightarrow -2 K=0$ or 16
$ \Rightarrow \, K =0$ or 8