| Find the area of \[\Delta ABC,\]whose vertices a-s \[A\,\,(8,-\,\,4),\]\[B\,\,(3,6)\]and \[C\,\,(-\,2,4).\] |
A) 30 sq units
B) 20 sq units
C) 10 sq units
D) 15 sq units
Correct Answer: A
Solution :
| Here, \[A\,\,(8-4),\] so \[{{x}_{1}}=8,\]\[{{y}_{1}}=-\,\,4\] |
| \[B\,\,(3,6),\]so \[{{x}_{2}}=3,\]\[{{y}_{2}}=6\] |
| \[C\,(-\,2,4),\]so \[{{x}_{3}}=-\,2,\]\[{{y}_{3}}=4\] |
| \[\therefore \]Area of \[\Delta ABC=\frac{1}{2}\{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})\]\[+\,\,{{x}_{3}}({{y}_{1}}-{{y}_{2}})\}\] |
| \[=\frac{1}{2}[8\,\,(6-4)+3\{4-(-\,\,4)\}+(-\,2)(-\,\,4-6)]\] |
| \[=\frac{1}{2}\{16+24+20\}=\frac{1}{2}\times 60=30\,\,\text{sq}\,\,\text{units}\] |
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