To calculate the area of a triangle on a coordinate plane, we can use the following 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 the coordinates of the three vertices of the triangle are $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$.

Based on your description:

• $(x_1, y_1) = (0, 0)$
• $(x_2, y_2) = (-2, 3)$
• $(x_3, y_3) = (5, 3)$

Substitute these values into the formula:

$\text{Area} = \frac{1}{2} \left| 0(3 - 3) + (-2)(3 - 0) + 5(0 - 3) \right|$

Now, let's compute the expression:

$\text{Area} = \frac{1}{2} \left| 0 + (-2)(3) + 5(-3) \right|$

$\text{Area} = \frac{1}{2} \left| 0 - 6 - 15 \right|$

$\text{Area} = \frac{1}{2} \left| -21 \right|$

$\text{Area} = \frac{1}{2} \times 21 = 10.5$

So, the area of the triangle is 10.5 square units.

Would you like to dive into the details or have any questions about the solution?

Here are some related questions:

1. How would the area formula change if the vertices were on a horizontal or vertical line?
2. What is the formula for the area of a triangle if the base and height are given?
3. How can you calculate the perimeter of a triangle on a coordinate plane?
4. How would the area change if the triangle was rotated?
5. Can the formula for the area of a triangle on the coordinate plane be used for non-right triangles?

Tip: Always double-check that your coordinates are entered in the correct order: $(x_1, y_1), (x_2, y_2), (x_3, y_3)$, and be sure to apply the formula carefully!