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 Tier II, 2014]

A) 1 sq unit

B) 2 sq units

C) 4 sq units

D) None of these

Correct Answer: A

Solution :

[a]        From the figure, triangle formed by the graph Straight lines \[=\Delta AOB\] Here,     \[{{x}_{1}}=1,\]\[{{y}_{1}}=1\] \[{{x}_{2}}=0,\]\[{{y}_{2}}=0\] \[{{x}_{3}}=0,\]\[{{y}_{3}}=0\] \[\therefore \]Area of \[\Delta AOB=\frac{1}{2}[{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})]\] \[=\frac{1}{2}[1\,(0-0)+0\,(0-1)+2\,(1-0)]\] \[=\frac{1}{2}[1\times 0+0\times -1+2\times 1]=\frac{1}{2}[0-0+2]\] \[=\frac{1}{2}\times 2=1\,sq\,unit\].