Foot of Perpendicular in Normal Form

Foot of Perpendicular in Normal Form

## Formula

For point $$(x_1,y_1)$$ and line:

$$x\cos\alpha+y\sin\alpha=p$$

the foot of perpendicular is:

$$\left(x_1-d\cos\alpha,y_1-d\sin\alpha\right)$$

where:

$$d=x_1\cos\alpha+y_1\sin\alpha-p$$

## Usage

- Used to locate the perpendicular projection of a point onto a line in normal form.