| Find the area of \[\Delta ABC\] whose vertices are\[A\,(8,-\,\,4),\]\[B\,(3,6)\]and \[C\,(-\,2,4).\] |
A) 40 sq units
B) 30 sq units
C) 20 sq units
D) 15 sq units
Correct Answer: B
Solution :
| Area of \[\Delta ABC=\frac{1}{2}\left| \{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}}) \right.\] |
| \[\left. +{{x}_{3}}({{y}_{1}}-{{y}_{2}})\} \right|\] |
| \[=\frac{1}{2}\left| \{8\,(6-4)+3\,(4+4-2\,(-\,4-6)\} \right|\] |
| \[=\frac{1}{2}\left| (8\times 2+3\times 8-2\times -10) \right|\] |
| \[=\frac{1}{2}\left| 16+24+20 \right|\] |
| \[=\frac{1}{2}\left| 60 \right|=30\,\,\text{sq}\,\,\text{units}\] |
You need to login to perform this action.
You will be redirected in
3 sec
