SSC
Quantitative Aptitude
Coordinate Geometry
Question Bank
Coordinate Geometry and Graphs of Linear Equations (II)
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 \[\Delta AOB=\frac{1}{2}[{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})]\] \[=\frac{1}{2}[1\,(0-0)+0\,(0-1)+2\,(1-0)]\] \[=\frac{1}{2}[1\times 0+0\times -1+2\times 1]=\frac{1}{2}[0-0+2]\] \[=\frac{1}{2}\times 2=1\,sq\,unit\]