To find the area of the triangle formed by the given vertices, we can use the coordinates of the vertices and apply the formula for the area of a triangle using its vertices:
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Identify the vertices:
- Vertex A (2, 1)
- Vertex B (10, 4)
- Vertex C (10, 7)
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Calculate the area using the determinant method: The formula for the area (A) of a triangle given vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is:
\[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Plugging in our vertex coordinates:
\[ A = \frac{1}{2} \left| 2(4 - 7) + 10(7 - 1) + 10(1 - 4) \right| \]
Simplifying this step by step:
\[ = \frac{1}{2} \left| 2(-3) + 10(6) + 10(-3) \right| \]
\[ = \frac{1}{2} \left| -6 + 60 - 30 \right| \]
\[ = \frac{1}{2} \left| 24 \right| = \frac{24}{2} = 12 \]
Thus, the area of the triangle is 12 square units.
Therefore, the correct answer is: 12 square units.