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  4. If the area of the triangle with vertices (x, 0)(1,1) (0,2) is 4 square units. Then the value of x is.

Q. If the area of the triangle with vertices $(x, 0)(1,1)\, \&\,(0,2)$ is $4$ square units. Then the value of $x$ is.

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Solution:

Area $=\frac{1}{2}\begin{vmatrix}x & 0 & 1 \\ 1 & 1 & 1 \\ 0 & 2 & 1\end{vmatrix}$
$4 =\frac{1}{2}[x(1-2)-0+1(2-0)]$
$8 =-x+2,$
$\therefore x =2-8, x =-6$

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