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(A) The vertices of the quadrilateral are formed by the intersection of the lines:$1$. $x=0$ and $y=0$ intersect at $B(0,0)$.$2$. $x=0$ and $6x+y=3$ i

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$3x - 2y = 0$

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(A) The vertices of the quadrilateral are formed by the intersection of the lines:$1$. $x=0$ and $y=0$ intersect at $B(0,0)$.$2$. $x=0$ and $6x+y=3$ intersect at $A(0,3)$.$3$. $y=0$ and $x+y=1$ intersect at $C(1,0)$.$4$. $x+y=1$ and $6x+y=3$ intersect at $D(\frac{2}{5}, \frac{3}{5})$.The diagonal passing through the origin $B(0,0)$ must also pass through the vertex $D(\frac{2}{5}, \frac{3}{5})$.The equation of a line passing through $(0,0)$ and $(x_1, y_1)$ is $y = \frac{y_1}{x_1}x$.Substituting $x_1 = \frac{2}{5}$ and $y_1 = \frac{3}{5}$:$y = \frac{3/5}{2/5}x$$y = \frac{3}{2}x$$2y = 3x$$3x - 2y = 0$.

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

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