| Find the area of a triangle whose vertices are \[(1,-1),\]\[(-\,\,4,6)\] and \[(-\,\,3,\,\,-5)\] |
A) 20 sq units
B) 22 sq units
C) 24 sq units
D) 3 sq units
Correct Answer: C
Solution :
| Area of triangle |
| \[=\frac{1}{2}\left| {{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}}) \right|\] |
| \[=\frac{1}{2}\left| 1\,\,(6+5)+(-\,\,4)(-\,\,5+1)+(-\,\,3)(-1-6) \right|\] |
| \[=\frac{1}{2}\left| 11+(-\,\,4)(-\,\,4)+(-\,\,3)(-\,\,7) \right|\] |
| \[=\frac{1}{2}\left| 11+16+21 \right|=\frac{1}{2}\left| 48 \right|=24\,\,\text{sq}\,\,\text{units}\] |
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