Question : The area of the triangle formed by the graph of the straight lines $x-y=0$, $x+y=2$, and the $x$-axis is:
Option 1: 1 sq. unit
Option 2: 2 sq. units
Option 3: 4 sq. units
Option 4: 5 sq. units
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Correct Answer: 1 sq. unit
Solution :
Given: The straight lines $x-y=0$, $x+y=2$.
By substituting $x=y$ in the equation $x+y=2$ , we get,
$2y=2$
⇒ $y=1$ and therefore, $x$ = 1
The point of intersection of two lines is $(1,1)$.
By substituting $y=0$ in the equation $x+y=2$, we get,
$x+0=2$
⇒ $x=2$
The point of intersection on $x$–axis is $(2,0)$.
So, the area of $\triangle OAC=\frac{1}{2} \times OA \times CD$.
Or, the area of $\triangle OAC=\frac{1}{2} \times 2 \times1$
The area of $\triangle OAC=1$ sq. unit
Hence, the correct answer is 1 sq. unit.
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