1. We are asked to find the area of a triangle with vertices at points (1, 0), (2, 2), and (3, 1) using the determinant method. 2. The formula for the area of a triangle given vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is: $$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$$ 3. Substitute the given points into the formula: $$x_1=1, y_1=0; \quad x_2=2, y_2=2; \quad x_3=3, y_3=1$$ 4. Calculate each term inside the absolute value: $$1(2 - 1) + 2(1 - 0) + 3(0 - 2) = 1(1) + 2(1) + 3(-2) = 1 + 2 - 6 = -3$$ 5. Take the absolute value and multiply by $\frac{1}{2}$: $$\text{Area} = \frac{1}{2} | -3 | = \frac{1}{2} \times 3 = 1.5$$ 6. Therefore, the area of the triangle is $1.5$ square units.