| The vertices of a triangle are \[A\,\,(4,4),\]\[B\,\,(3,-\,\,2)\] and \[C\,\,(-\,\,3,16).\]The area of the triangle is |
A) 30 sq units
B) 36 sq units
C) 27 sq units
D) 40 sq units
Correct Answer: C
Solution :
| Let \[{{x}_{1}}=4,\]\[{{x}_{2}}=3\]and \[{{x}_{3}}=-\,\,3,\] |
| \[{{y}_{1}}=4,\]\[{{y}_{2}}=-\,\,2\]and \[{{y}_{3}}=16\] |
| \[\therefore \]Area of triangle |
| \[=\left| \frac{1}{2}\{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})\} \right|\] |
| \[=\left| \frac{1}{2}\{4\,\,(-\,\,2-16)+3\,\,(16-4)+(-3)(4+2)\} \right|\] |
| \[=\left| \frac{1}{2}(-72+36-18) \right|=\left| \frac{1}{2}\times (-\,\,54) \right|=27\,\,\text{sq}\,\,\text{units}\] |
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