Distance Formula Between a Point and a Line
The shortest distance between a point and a line can easily be calculated using the distance formula discussed in this section of the article. The distance between a point and the line can be in 2D or 3D space.
Let’s learn about the distance of a point to a line in 2D and 3D in this article.
Distance Formula From a Point To a Line in 2D
The distance between a point and a line in 2D is calculated using the formula discussed below:
Let’s take a point (x1, y1) and a line ax + by + c = 0 then the distance between them is given using the Distance Formula:
d =
Distance Formula From a Point To a Line in 3D
We can also calculate the distance of a point from the line in the 3D plane.
Let’s take a point A (x1, y1, z1) and a line (x – x2)/a = (y – y2)/b = (z – z2)/c in the 3D plane then the distance between them is given using the Distance Formula:
Where,
- A is the point (x1, y1, z1) from which the distance is to be calculated
- Q is the point (x2, y2, z2) on the line L from which distance is calculated
- is (x2 -x1, y2 – y1, z2 – z1)
- is the direction vector of the line <a, b, c>
Distance Formula in Coordinate Geometry
Distance Formula in Coordinate Geometry is used to compute the distance between two points, a point, and a line, and two line segments. The distance formula is based on the Pythagorean theorem. In the formula, d represents the distance, y2 is the y-coordinate of the second point, y1 is the y-coordinate of the first point, x2 is the x-coordinate of the second point, and x1 is the x-coordinate of the first point.
Coordinate geometry, commonly referred to as analytic geometry or Cartesian geometry, is a branch of geometry based on a coordinate system. Its applications include physics, engineering, air travel, rocketry, space research, and spaceflight.
In this article, we will learn about the distance between two points in coordinate geometry, the formula for the distance between two points, a point, a line, a point and a plane, and others in detail.
Table of Content
- What is Distance Formula in Coordinate Geometry?
- Coordinate Distance Calculator
- Distance Between Two Points Formula
- Distance Formula Between Two Points in 2D
- Distance Formula Between Two Points in 3D
- Distance between Two Points in Polar Co-ordinates
- Distance Formula Between a Point and a Line
- Distance Between Two Lines
- Distance From a Point To a Plane
- Distance Between Two Parallel Planes
- Applications of Distance Formula in Coordinate Geometry
- Solved Questions on Distance Formula in Coordinate Geometry
- Practice Problems on Distance Formula in Coordinate Geometry
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