# Area of Triangle in Determinant Form/Examples

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## Examples of Area of Triangle in Determinant Form

### Vertex at Origin

Let $A = \tuple {0, 0}, B = \tuple {b, a}, C = \tuple {x, y}$ be points in the Cartesian plane.

Let $T$ the triangle whose vertices are at $A$, $B$ and $C$.

Then the area $\mathcal A$ of $T$ is:

$\map \Area T = \dfrac {\size {b y - a x} } 2$

### Vertices at $\paren {-4 - i}, \paren {1 + 2 i}, \paren {4 - 3 i}$

Let $T$ be a triangle embedded in the complex plane with vertices at $\paren {-4 - i}, \paren {1 + 2 i}, \paren {4 - 3 i}$.

The area of $T$ is given by:

$\map \Area T = 17$