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A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .
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.
The intersection point falls within the first line segment if 0 ≤ t ≤ 1, and it falls within the second line segment if 0 ≤ u ≤ 1. These inequalities can be tested without the need for division, allowing rapid determination of the existence of any line segment intersection before calculating its exact point. [3]
Common lines and line segments on a circle, including a secant. A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line. A chord is the line segment that joins two distinct points of a circle. A chord is ...
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 point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...
A line arrangement in the projective plane differs from its Euclidean counterpart in that the two Euclidean rays at either end of a line are replaced by a single edge in the projective plane that connects the leftmost and rightmost vertices on that line, and in that pairs of unbounded Euclidean cells are replaced in the projective plane by ...
President-elect Donald Trump campaigned on the promise to create more American jobs and protect existing ones. But many of his proposals and expected policy changes threaten to have the opposite ...
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 point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...