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Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0. We can represent these two lines in line coordinates as U 1 = (a 1, b 1, c 1) and U 2 = (a 2, b 2, c 2). The intersection P′ of two lines is then simply given by [4]
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 ).
A cross is a compound geometrical figure consisting of two intersecting lines, usually perpendicular to each other. The lines usually run vertically and horizontally. A cross of oblique lines, in the shape of the Latin letter X, is termed a saltire in heraldic terminology.
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
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 ...
intercept theorem with a pair of intersecting lines intercept theorem with more than two lines. The first two statements remain true if the two rays get replaced by two lines intersecting in . In this case there are two scenarios with regard to , either it lies between the 2 parallels (X figure) or it does not (V figure).
Two intersecting lines can degenerate to two parallel lines, by rotating until parallel, as in =, or to a double line by rotating into each other about a point, as in =, in each case as a goes to 0. Two parallel lines can degenerate to a double line by moving into each other, as in x 2 − a 2 = 0 {\displaystyle x^{2}-a^{2}=0} as a goes to 0 ...
The Greek cross is an equal-armed cross with the lines running vertically and horizontally. The saltire is a diagonal equal-armed cross, sometimes with the two intersecting lines that are not perpendicular to each other. Equal-armed crosses are symbols that have been found since ancient times in different cultures and traditions throughout the ...