To find the area of the triangle formed by the points A (0, 3), B (10, 6), and C (6, 3), we can use the formula for the area of a triangle given its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Substituting in the coordinates of points A, B, and C:
- \(A (0, 3)\): \(x_1 = 0, y_1 = 3\)
- \(B (10, 6)\): \(x_2 = 10, y_2 = 6\)
- \(C (6, 3)\): \(x_3 = 6, y_3 = 3\)
Now substituting these values into the formula:
\[ \text{Area} = \frac{1}{2} \left| 0(6 - 3) + 10(3 - 3) + 6(3 - 6) \right| \]
Calculating each term:
- First term: \(0(6 - 3) = 0\)
- Second term: \(10(3 - 3) = 0\)
- Third term: \(6(3 - 6) = 6 \times -3 = -18\)
Now, substituting back into the equation:
\[ \text{Area} = \frac{1}{2} \left| 0 + 0 - 18 \right| = \frac{1}{2} \left| -18 \right| = \frac{1}{2} \times 18 = 9 \]
Thus, the area of the triangle is 9 square units. The closest answer choice is:
- 09