What is the area of the triangle whose vertices are \(A(-2,\,6)\), \(B(-4,\,-2)\) and \(C(5,\,1)\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 33 square units
The area of a triangle with vertices \((x_1,\,y_1)\), \((x_2,\,y_2)\), \((x_3,\,y_3)\) is \(\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|\); the absolute value is taken because an area cannot be negative.
Term from A: \(-2(-2-1)=-2\times(-3)=6\)
Term from B: \(-4(1-6)=-4\times(-5)=20\)
Term from C: \(5(6-(-2))=5\times8=40\)
Sum of the terms: \(6+20+40=66\)
Area \(\displaystyle =\frac{1}{2}\times|66|=33\) square units
