Question

The area of the triangle whose sides are represented by the graphs of the equations $x=0,y=0$ and $x+y=2$, is

• A. 4 sq.units
• B. 3 sq.units
• C. 2 sq.units
• D. 5 sq.units

Answer 1

The correct option is C 2 sq.units

The equation x = 0 represents y-axis, and the equation y = 0 represents x-axis.
For the equation $x+y=2:$
At $x=0;0+y=2$
$\Rightarrow y=2$
At $y=0;x+0=2$
$\Rightarrow x=2$
$\begin{array}{ccc}x& 0& 2\\ y& 2& 0\end{array}$
Drawing the lines $x=0,y=0$ and $x+y=2$ on the coordinate plane, we get

From the obtained graph, the formed triangle has a height of 2 units and base length of 2 units.
$\therefore$ Area of a Triangle $=\frac{1}{2}\times \text{Base}\times \text{Height}$
$=\frac{1}{2}\times 2\times 2$
$=2$ sq.units
Hence, the correct answer is option (c).