question_answer

Area of the triangle formed by the graph of the straight lines \[x-y=0,\]\[x+y=2\] and the X-axis is

[SSC (CGL) Mains 2014]

A) 1 sq unit           

B) 2 sq units

C) 4 sq units                      

D) None of the above

Correct Answer: A

Solution :

From figure,

\[\Delta AOB\] is made by given lines, where A (1, 1), O(0, 0) and B (2, 0) are coordinates.

Here,     \[{{x}_{1}}=1,\]\[{{y}_{1}}=1,\]\[{{x}_{2}}=0\]

\[{{y}_{2}}=0,\]\[{{x}_{3}}=2,\]\[{{y}_{3}}=0\]

\[\therefore \] Area of \[\Delta AOB=\frac{1}{2}\,\,[{{x}_{1}}({{y}_{2}}-{{y}_{3}})\]

\[+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})]\]

\[=\frac{1}{2}[1\,(0-0)+0\,(0-1)+2\,(1-0)]\]

\[=\frac{1}{2}[1\times 0+0\times (-1)+2\times 1]\]

\[=\frac{1}{2}\,\,[0-0+2]=\frac{1}{2}\times 2=1\,\text{sq}\,\text{unit}\]