The area of the triangle whose vertices are given by the coordinates (1, 2), (-4, -3) and (4, 1) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10 sq. units
For a triangle with vertices \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\), the area formula is
\(\displaystyle \text{Area}=\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|\)
The modulus sign is there because the bracket can come out negative when the vertices are taken clockwise; an area is never negative. Here \((x_1,y_1)=(1,2)\), \((x_2,y_2)=(-4,-3)\) and \((x_3,y_3)=(4,1)\).
Term of the first vertex: \(1\times(-3-1)=-4\)
Term of the second vertex: \((-4)\times(1-2)=4\)
Term of the third vertex: \(4\times(2-(-3))=20\)
Area, half of their sum taken as positive: \(\displaystyle \frac{1}{2}\left|-4+4+20\right|=\frac{20}{2}=10\) sq. units