What is the area of the triangle whose vertices are \(A(1,\,-2)\), \(B(5,\,1)\) and \(C(-1,\,4)\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15 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: \(1(1-4)=1\times(-3)=-3\)
Term from B: \(5(4-(-2))=5\times6=30\)
Term from C: \(-1(-2-1)=-1\times(-3)=3\)
Sum of the terms: \(-3+30+3=30\)
Area \(\displaystyle =\frac{1}{2}\times|30|=15\) square units
