Q15 / 109 · NTA Abhyas (JEE Main) 2020 · Mathematics · Straight Lines

The line $x = \frac{c}{2}$ 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

A
$30$
Correct answer
B
$6$
C
$\frac{7}{2}$
D
$15$

Solution

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

$\Rightarrow c = 6$

Hence, the correct answer is option: 'B'.

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Solution

More Straight Lines Questions

The line $x = \frac{c}{2}$ 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