Question

What is the area of the triangle in square units?
18
15
6
9
points (0,3) (10,6) (6,3)

Answer 1

To find the area of a triangle defined by three vertices in a Cartesian coordinate system, 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 of the triangle.

In your case, the vertices of the triangle are:

- \( (0, 3) \)
- \( (10, 6) \)
- \( (6, 3) \)

Let's assign:

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

Now, substitute these values into the area formula:

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

Calculating each term:

1. \( 0(6-3) = 0 \)
2. \( 10(3-3) = 0 \)
3. \( 6(3-6) = 6 \cdot (-3) = -18 \)

Now plug these values into the 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:

\[
\boxed{9} \text{ square units}
\]