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  4. The line x=(c/2) divides the triangle with vertices (0,0),(1,1) and (9,1) into two regions. If the area of the two regions is the same, then c is equal to

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Q. The line $x=\frac{c}{2}$ divides the triangle with vertices $\left(0,0\right),\left(1,1\right)$ and $\left(9,1\right)$ into two regions. If the area of the two regions is the same, then $c$ is equal to

NTA AbhyasNTA Abhyas 2020Straight Lines

Solution:

$$ Solution
$2 \cdot \frac{1}{2} \cdot \begin{vmatrix} 9 & 1 & 1 \\ \frac{c}{2} & 1 & 1 \\ \frac{c}{2} & \frac{c}{18} & 1 \end{vmatrix} = \frac{1}{2} \begin{vmatrix} 9 & 1 & 1 \\ 1 & 1 & 1 \\ 0 & 0 & 1 \end{vmatrix} = \frac{1}{2} \cdot 8 = 4$
$\Rightarrow \frac{c}{2}=3$ or $\frac{c}{2}=15$ (not possible)
$\Rightarrow c=6$