Point Equidistant from Two Lines

Point Equidistant from Two Lines

## Formula

For lines:

$$L_1=A_1x+B_1y+C_1=0$$

and:

$$L_2=A_2x+B_2y+C_2=0$$

a point $$(x,y)$$ equidistant from them satisfies:

$$\frac{|L_1|}{\sqrt{A_1^2+B_1^2}}=\frac{|L_2|}{\sqrt{A_2^2+B_2^2}}$$

## Usage

- Used to derive the angle bisectors or loci based on equal distances from two lines.