Find the area of the triangle formed by the lines whose equations are 2y - x = 5, y + 2x =7 and y - x = 1.

$\frac{3}{10}$

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$\frac{2}{5}$

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Solution

The correct option is A
$\frac{3}{10}$

Let the equations of the sides BC, CA and AB of the triangle ABC be represented by
2y - x = 5 ...(1)
y + 2x = 7...(2)
y - x = 1 ......(3)
Solving the above 3 equations (1),(2)and(3),we get A(2, 3), B(3, 4) and $C (\frac{9}{5}, \frac{17}{5}) = \frac{1}{2} {2 \times 4 - 3 \times 3 + 3 \times \frac{17}{5} - 4 \times \frac{9}{5} + \frac{9}{5} \times 3 - \frac{17}{5} \times 2} = \frac{1}{2} (8 - 9 + \frac{51}{5} - \frac{36}{5} + \frac{27}{5} - \frac{34}{5}) = \frac{3}{10} u n i t s .$

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