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In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both ...
Here, p is the (positive) length of the line segment perpendicular to the line and delimited by the origin and the line, and is the (oriented) angle from the x-axis to this segment. It may be useful to express the equation in terms of the angle α = φ + π / 2 {\displaystyle \alpha =\varphi +\pi /2} between the x -axis and the line.
Secant line. In geometry, a secant is a line that intersects a curve at a minimum of two distinct points. [ 1] The word secant comes from the Latin word secare, meaning to cut. [ 2] In the case of a circle, a secant intersects the circle at exactly two points. A chord is the line segment determined by the two points, that is, the interval on ...
Intersection (geometry) The red dot represents the point at which the two lines intersect. In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Line–line intersection. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection . In three-dimensional Euclidean geometry, if two lines are not in ...
Tangent lines to circles. In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.
When rectified, the curve gives a straight line segment with the same length as the curve's arc length. Arc length sof a logarithmic spiralas a function of its parameter θ. Arc lengthis the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected ...