To find the area of a triangle given its vertices, we can use the formula:
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
where \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are the coordinates of the vertices A, B, and C, respectively.
Given the points:
- \( A(0, 3) \) \( (x_1 = 0, y_1 = 3) \)
- \( B(10, 6) \) \( (x_2 = 10, y_2 = 6) \)
- \( C(6, 3) \) \( (x_3 = 6, y_3 = 3) \)
Plugging in these coordinates into the area formula:
\[ \text{Area} = \frac{1}{2} \left| 0(6 - 3) + 10(3 - 3) + 6(3 - 6) \right| \]
Calculating each term:
- \( 0(6 - 3) = 0 \)
- \( 10(3 - 3) = 10 \cdot 0 = 0 \)
- \( 6(3 - 6) = 6 \cdot -3 = -18 \)
Now substituting these values back into the area formula:
\[ \text{Area} = \frac{1}{2} \left| 0 + 0 - 18 \right| = \frac{1}{2} \left| -18 \right| = \frac{1}{2} \cdot 18 = 9 \]
Thus, the area of the triangle is \( \text{9} \) square units.
The answer is: B. 9.
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