Line (geometry)
A line in geometry is a one-dimensional figure that extends infinitely in both directions and has no endpoints, width, or curvature. It is defined by any two distinct points on it and is the shortest path between those points when considered in a straight path. Lines are foundational to Euclidean geometry and are used to construct angles, polygons, and coordinate systems.
Key Formula
y = mx + b
LaTeX: y = mx + b
| Symbol | Meaning | Unit |
|---|---|---|
| y | y-coordinate of any point on the line | unitless |
| m | slope of the line | unitless |
| x | x-coordinate of any point on the line | unitless |
| b | y-intercept (where line crosses y-axis) | unitless |
Worked Example
Problem
Find the equation of the line passing through points (2, 3) and (4, 7).
Solution
Step 1: Find the slope: m = (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4 / 2 = 2. Step 2: Use point-slope form with point (2, 3): y - 3 = 2(x - 2). Step 3: Simplify: y - 3 = 2x - 4, so y = 2x - 1.
Answer
y = 2x - 1
Types of Lines in Geometry
| Type | Symbol | Description | Example |
|---|---|---|---|
| Line | ↔ AB | Extends infinitely in both directions | x-axis |
| Line segment | AB | Has two definite endpoints | Side of a triangle |
| Ray | → AB | One endpoint, extends infinitely in one direction | Sun's ray |
| Parallel lines | l ∥ m | Never intersect, same slope | Railway tracks |
| Perpendicular lines | l ⊥ m | Intersect at 90° | Corner of a room |
| Intersecting lines | — | Cross at one point | Road crossing |
Interactive Tools
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Related Terms
Point (geometry)
A point is a fundamental geometric object that has no dimensions — no length, width, or height — and represents an exact location in space. It is typically denoted by a capital letter and is the most basic building block of all geometric figures. Points are used to define lines, planes, shapes, and every other geometric construction.
Plane (geometry)
A plane in geometry is a flat, two-dimensional surface that extends infinitely in all directions and has no thickness. It is determined uniquely by any three non-collinear points, by a line and a point not on that line, or by two intersecting or parallel lines. Planes are essential in three-dimensional geometry for describing surfaces, intersections, and spatial relationships.
Angle
An angle is the measure of rotation between two rays (sides) that share a common endpoint called the vertex. Angles are measured in degrees (°) or radians (rad) and describe the amount of turn between two directions. They are fundamental to geometry, trigonometry, physics, and engineering, appearing in everything from architectural blueprints to robotic arm movements.
From Latin "linea" meaning a linen thread, string, or boundary line, derived from "linum" meaning flax (from which linen was made). The geometric sense evolved to mean any straight mark or path. Greek geometers used "gramme" for line.