The diagonal passing through origin of a quadrilateral formed by $x = 0, y = 0, x + y = 1$ and $6 x + y = 3$ is

3 x - 2 y = 0

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2 x - 3 y = 0

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3 x + 2 y = 0

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None of these

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Solution

The correct option is A $3 x - 2 y = 0$
Let us find the Point opposite to origin in the Quadrilateral which will be the intersection of $x + y = 1, 6 x + y = 3$

Hence, Solving the Above Equation Simulataneously
$x = \frac{2}{5}, y = \frac{3}{5}$

Now, The Slope of Required Diagonal
$= \frac{\frac{3}{5} - 0}{\frac{2}{5} - 0} = \frac{3}{2}$

Hence, Equation of Diagonal
$(y - 0) = \frac{3}{2} (x - 0) \Rightarrow 2 y = 3 x \Rightarrow 3 x - 2 y = 0$

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Similar questions

3 x + 2 y = 6

x + y = 5, y - 2 x = 8, 3 y + 2 x = 0

4 y - x = 0

x^{2} + y^{2} - 6 x + 2 y - 8 = 0

X = 0, Y = 0, X + Y - 1 = 0

6 x + Y - 3 = 0

Solve for x and y:

$\frac{1}{2 x} + \frac{1}{3 y} = 2, \frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6} (x \neq 0, y \neq 0) .$

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