Find the area (in square units) of a triangle whose vertices are A (2, 4), B (3, 5) and C (−1, 3).
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
The coordinate formula for the area of a triangle works straight from the three vertices, without drawing. For vertices \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\), the area of the triangle is \(\displaystyle\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|\).
Term for A(2, 4): \(2\times(5-3)=4\)
Term for B(3, 5): \(3\times(3-4)=-3\)
Term for C(−1, 3): \(-1\times(4-5)=1\)
Half the absolute value of their sum: area \(=\displaystyle\frac{1}{2}\left|4-3+1\right|=\frac{1}{2}\times2=1\) square unit