What is Distance Between Two Lines?
Distance between two parallel lines is the distance of the perpendicular drawn from one point of the line to a point on another line. It is the shortest distance between two lines. To measure the distance between two parallel lines. Let’s take two arbitrary parallel lines. Two parallel lines will have the same slope. The equation of a line is y = mx + c. Let equations of the two lines are,
- y = mx + c1
- y = mx + c2
The images for the same equations are added below,
As shown in the above figure, the two lines are drawn with a slope equal to m. The distance between them has been taken as d. The line y = mx + c1 intercepts the y-axis at the point A(0, c1) and the other line y = mx + c2 intercepts the y-axis at B(0, c2). The length AB is given by c2 – c1, d can be calculated using trigonometry considering the triangle ABC. Considering the triangle ABC,
d = AB × cos θ
d = (c2 – c1) × cos θ.
d = (c2 – c1)/ (sec θ); since, cos θ = 1/sec θ.
d = (c2 – c1) / √(1 + tan2 θ); since, sec2 θ = 1 + tan2 θ.
d = (c2 – c1)/√(1 + m2)
Distance Between Two Lines
Distance between two is the perpendicular distance between the two lines. Here, we consider finding distance between two parallel lines. Parallel lines are lines that have similar slopes. Parallel lines are non-intersecting lines, and they meet at infinity. The distance between two parallel lines is the shortest distance between two lines. In this article, we will learn about parallel lines, the Distance between Parallel Lines, Examples, and others in detail.
Table of Content
- What are Parallel Lines?
- Distance Between Two Parallel Lines
- How to Find Distance Between Two Lines
- Distance Between Two Lines in 3d
- Shortest Distance Between Two Skew Lines