A) \[\frac{15}{2}\]
B) \[\frac{13}{7}\]
C) \[\frac{21}{2}\]
D) \[\frac{23}{2}\]
Correct Answer: C
Solution :
Let \[A=({{x}_{1}},{{y}_{1}})=(2,3),\]\[B=({{x}_{2}},{{y}_{2}})\] \[=(-1,0),\]\[C=({{x}_{3}},{{x}_{3}})=(2-4)\] Area of \[\Delta ABC=\frac{1}{2}[{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}\]\[({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})]\] \[=\frac{1}{2}[2\,\,(0+4)+(-1)(-4-3)+2\,\,(3-0)]\] \[=\frac{1}{2}(8+7+6)=\frac{21}{2}\]sq units
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