Question

Question 12
Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y - axis, find the area of this triangle?

Answer 1

The given pair of linear equations
Table for line 2x + y = 4,
$\begin{array}{ccc}x& 0& 2\\ y=4-2x& 4& 0\\ Points& A& B\end{array}$
And table for line 2x – y = 4
$\begin{array}{ccc}X& 0& 2\\ y=2x-4& -4& 0\\ Points& C& B\end{array}$

Graphical representation of both lines
Here, both lines and y – axis from a $\Delta$ ABC
Hence, the vertices of $\Delta$ABC are A(0, 4) B (2, 0) and C (0, - 4)
$\therefore$ Required area of $\Delta$ ABC = 2 $\times$ Area of $\Delta$ AOB
$=2\times \frac{1}{2}\times 4\times 2=8squnits$
Hence, the required area of the triangle is 8 sq units