Distance Formula Between Two Points in 3D
In a 3D plane, we use three coordinates to define the position of any point. Now to find the distance between two points in 3D lets first take two points A (x1, y1, z1) and B (x2, y2, z2) then the shortest distance between these two points AB in 3D is given using the Distance Formula:
d = √[(x2 – x1)2 + (y2 – y1)2 + (z2 -z1)2]
where d is the shortest distance between points A and B.
Example: Find the distance between point A (2, 5, 6) and point B (3, 4, 8).
Solution:
Distance between points A and B is given using the formula,
d = √[(x2 – x1)2 + (y2 – y1)2 + (z2 -z1)2]
given points, A (2, 5, 6) and B (3, 4, 8), comparing with A (x1, y1, z1) and B (x2, y2, z2)
we get, x1 = 2, y1 = 5, z1 = 6 and x2 = 3, y2 = 4, z2 = 8 substituting these values in the above formula we get,
d = √[(3-2)2 + (4-5)2 + (8-6)2]
⇒ d = √[(1)2 + (-1)2 + (2)2]
⇒ d = √[1 + 1 + 4]
⇒ d = √(6) unit
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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