Question

B (10, 6)
6-
4-
A (0, 3)
2-
C(6, 3)
2
4
6
8
10½2
What is the area of the triangle in square units?
(1 point)
• 15
09
018
06
Ignore the extra numbers

Answer 1

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:

1. First term: \(0(6 - 3) = 0\)
2. Second term: \(10(3 - 3) = 0\)
3. 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**