Determinant Form for Intersection Coordinates

Determinant Form for Intersection Coordinates

## Formula

For two lines:

$$A_1x+B_1y+C_1=0$$

and:

$$A_2x+B_2y+C_2=0$$

their intersection satisfies:

$$x=\frac{\begin{vmatrix}-C_1&B_1\\-C_2&B_2\end{vmatrix}}{\begin{vmatrix}A_1&B_1\\A_2&B_2\end{vmatrix}}$$

$$y=\frac{\begin{vmatrix}A_1&-C_1\\A_2&-C_2\end{vmatrix}}{\begin{vmatrix}A_1&B_1\\A_2&B_2\end{vmatrix}}$$

## Usage

- Used to obtain the intersection point using determinant notation.