Question

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

• A. $3x–2y=0$
• B. $2x–3y=0$
• C. $3x+2y=0$
• D. None of these

Answer 1

The correct option is A

$3x–2y=0$

Explanation for the correct option:

Step:1 Finding the point of intersection

Given $6x+y=3$ and$x+y=1$

By subtracting the equations we get

$$\begin{gathered} 6x+y-x-y=3-1 \\ \Rightarrow x=\frac{2}{5} \\ \Rightarrow y=\frac{3}{5} \end{gathered}$$

​Step 2: Finding Slope of Diagonal

The slope is given by $\frac{{\displaystyle x_2}-x_1}{{\displaystyle y_2}-y_1}$

To find the slope let's consider

$x_2=\frac{2}{5},y_2=\frac{3}{5}$ and $x_1=0,y_1=0$ [given]

Now, the slope of the required diagonal is

$$\begin{gathered} =\frac{{\displaystyle \frac{3}{5}}-0}{{\displaystyle \frac{2}{5}}-0} \\ =\frac{3}{2} \end{gathered}$$

Step 3: Finding the equation of the diagonal

Hence, the equation of Diagonal is

$\left(y-y_1\right)=m\left(x-x_1\right)$

$$\begin{gathered} (y-0)=\frac{3}{2}(x-0) \\ \Rightarrow 2y=3x \\ \Rightarrow 3x-2y=0 \end{gathered}$$

Hence, option (A) is the correct answer.