What is the area of a triangle with vertices at (-4, 2), (5, 0), and (1, -3)?

To find the area of a triangle given its vertices, one effective method is to use the formula:

[

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

]

For the triangle with vertices at (-4, 2), (5, 0), and (1, -3), we can denote these points as follows:

1. ( (x_1, y_1) = (-4, 2) )

2. ( (x_2, y_2) = (5, 0) )

3. ( (x_3, y_3) = (1, -3) )

Plugging these coordinates into the area formula:

1. First, calculate the terms:

• ( y_2 - y_3 = 0 - (-3) = 3 )

• ( y_3 - y_1 = -3 - 2 = -5 )

• ( y_1 - y_2 = 2 - 0 = 2 )