Question

What is the area of the triangle in square units?

Point a(0,3)
Point B(10,6)
Point C (6,3)

(1 point)
18
9
15
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 our points:
- \(A(0,3) \rightarrow (x_1, y_1) = (0, 3)\)
- \(B(10,6) \rightarrow (x_2, y_2) = (10, 6)\)
- \(C(6,3) \rightarrow (x_3, y_3) = (6, 3)\)

Now plug in these values:

\[
\text{Area} = \frac{1}{2} \left| 0(6 - 3) + 10(3 - 3) + 6(3 - 6) \right|
\]
\[
= \frac{1}{2} \left| 0 + 10(0) + 6(-3) \right|
\]
\[
= \frac{1}{2} \left| 0 + 0 - 18 \right|
\]
\[
= \frac{1}{2} \left| -18 \right|
\]
\[
= \frac{1}{2} \times 18 = 9
\]

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