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With reference to the conventional Cartesian \((x,y)\) coordinate system, the vertices of a triangle have coordinates \((1,0)\), \((2,2)\), and \((4,3)\). The area of the triangle is equal to

1. 3/2
2. 3/4
3. 4/5
4. 5/2

Correct answer: 3/2

Solution

Using the coordinate area formula, the area is \(\frac12 |x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\). Substituting the points gives \(\frac12 |1(2-3)+2(3-0)+4(0-2)|=\frac12 |-1+6-8|=\frac32\). So the area is \(3/2\).

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