Question

What is the area of the triangle in square units?
A (0,3) B (10,6) C (6,3)
Answers are 15, 18, 9, 6

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:

\[
\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

Substituting in the coordinates \( A(0, 3) \), \( B(10, 6) \), and \( C(6, 3) \):

- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (10, 6) \)
- \( (x_3, y_3) = (6, 3) \)

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 area formula:

\[
\text{Area} = \frac{1}{2} \left| 0 + 0 - 18 \right| = \frac{1}{2} \left| -18 \right| = \frac{1}{2} \times 18 = 9
\]

Thus, the area of the triangle is \( \boxed{9} \) square units.