area of a triangle on a coordinate plane

1. Identify the vertices of the triangle: By observing the graph, we can identify the coordinates of the three vertices of the triangle. Let's label them A, B, and C.
Vertex A is at $(-1, 1)$.
Vertex B is at $(3, 1)$.
Vertex C is at $(1, -3)$.

2. Determine the base of the triangle: The base of the triangle can be considered the horizontal segment connecting vertices A and B, as they share the same y-coordinate. The length of the base is the absolute difference of their x-coordinates.
Base length = $|3 - (-1)| = |3 + 1| = 4$ units.

3. Determine the height of the triangle: The height of the triangle is the perpendicular distance from the third vertex (C) to the line containing the base (the line $y=1$). The y-coordinate of vertex C is $-3$, and the y-coordinate of the base is $1$. The height is the absolute difference of these y-coordinates.
Height = $|1 - (-3)| = |1 + 3| = 4$ units.

4. Calculate the area of the triangle: The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.
Area = $\frac{1}{2} \times 4 \times 4$
Area = $\frac{1}{2} imes 16$
Area = $8$ square units.