What is the area of the triangle whose vertices are \(A(-3,\,1)\), \(B(5,\,3)\) and \(C(1,\,-5)\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 28 square units
The area of the triangle with vertices \((x_1,\,y_1)\), \((x_2,\,y_2)\), \((x_3,\,y_3)\) is \(\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|\).
\(x_1(y_2-y_3)=-3\,(3-(-5))=-3\times8=-24\)
\(x_2(y_3-y_1)=5\,(-5-1)=5\times(-6)=-30\)
\(x_3(y_1-y_2)=1\,(1-3)=-2\)
Sum \(=-24-30-2=-56\)
Area \(\displaystyle =\frac{1}{2}\times|-56|=28\) square units
