Find the area (in square units) of a triangle whose vertices are (1, -1), (-4, 6) and (-3, -5).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24
The area of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\) and \((x_3, y_3)\) is given by the coordinate formula \(\displaystyle \frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|\). The modulus is taken because an area cannot be negative.
With A(1, −1), B(−4, 6) and C(−3, −5):
\(x_1(y_2-y_3)=1\times(6+5)=11\)
\(x_2(y_3-y_1)=-4\times(-5+1)=16\)
\(x_3(y_1-y_2)=-3\times(-1-6)=21\)
Area \(\displaystyle =\frac{1}{2}\times(11+16+21)=\frac{48}{2}=24\) square units
