Answer:
6.5 square units
Step-by-step explanation:
To find the area of a triangle given the coordinates of its vertices, we can use the following formula:
[tex]\textsf{Area} = \dfrac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|[/tex]
where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the coordinates of the vertices.
In this case:
- (x₁, y₁) = (-5, 1)
- (x₂, y₂) = (0, 0)
- (x₃, y₃) = (-3, -2)
Substitute the coordinates into the formula and solve for area:
[tex]\textsf{Area} = \dfrac{1}{2} |-5(0 - (-2)) + 0(-2 - 1) + (-3)(1 - 0)|\\\\\\\textsf{Area} = \dfrac{1}{2} |-5(2) + 0(-3) + (-3)(1)|\\\\\\\textsf{Area} = \dfrac{1}{2} |-10 +0 -3|\\\\\\\textsf{Area} = \dfrac{1}{2} |-13|\\\\\\\textsf{Area} = \dfrac{1}{2} \cdot 13\\\\\\\textsf{Area} = \dfrac{13}{2}=6.5\; \sf square\;units[/tex]
Therefore, the area of the triangle is:
[tex]\Large\boxed{\boxed{6.5\; \sf square\;units}}[/tex]
