# Lines, Planes, & Space

### Lines

A line is a one-dimensional figure. That is, a line has length, but no width or height. Basically, a line is made up of an infinite number of points. Points in the same line are called colinear. Between each point is another point. This continues on forever. You can never run out of points to discover in a line. However, when you are talking about points as dots, you can get something called a discrete line. A discrete line is a line made up of dots with space between the centers of the dots. A dense line is a line that is the shortest path between two points. The number line, or coordinatized line, is a line where every point is represented by a number and vice versa. The number line is a one-dimensional graph. See the paragraph about nodes to find out about networks and arcs.

If you have two points A and B, the line that contains them is the set of points consisting of the distinct points A and B, all of the points between them, all points for which A is between them and B, and all points for which B is between them and A. A line like that would be written . A line, if not made up by previously known points, can be represented by a single lowercase letter. This is as a contrast to the uppercase letters that represent points. A line segment is the set of points consisting of A, B, and all points between them. A line segment is written . If you have two points A and B, the ray that contains them is the set of points consisting of the distinct points A and B, all of the points between them, and all points for which B is between them and A. This is written .

Every line is either horizontal, vertical or oblique. Horizontal and vertical speak for themselves, and an oblique line is any line that isn't horizontal or vertical. Horizontal lines have a slope of zero. Vertical lines are said to have infinite slope, because they just go straight up and not over. People just can't stand that zero in the denominator. Here's something I bet you didn't know: In space, vertical lines never meet (they just go straight up/down), but it is possible for horizontal lines to meet (check out the corner of the ceiling - two horizontal lines meet there (the edge of the two walls)). Okay, so maybe you did know that.

There are four different relationships that two lines can have. Lines can be identical, intersecting, parallel, perpendicular, or skew. Identical lines are lines that coincide. Therefore, they are the same line. The second one is the most obvious. Intersecting lines are lines that share a point. Parallel lines are coplanar lines that never intersect. They always have a certain distance between them and always have the same direction. See the page on parallel lines for more information. Perpendicular lines are lines that intersect in one point and form a 90 degree angle while they're at it. They have a page of their own, too. Skew lines only happen in space. They are noncoplanar lines that never intersect. Unlike parallel lines, however, they don't always have a set distance between them, nor do they always have the same direction.

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### Planes

Planes are two-dimensional. A plane has length and width, but no height, and extends infinitely on all sides. Planes are thought of as flat surfaces, like a table top. A plane is made up of an infinite amount of lines. Two-dimensional figures are called plane figures. While this really should be in Algebra, coordinate planes are two-dimensional graphs that use the ordered pair to locate points. Another name for coordinate planes are Cartesian planes.

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### Space

There's been a request to add something about space here. Space is the set of all points. It is made up of an infinite number of planes.Figures in space are called solids or surfaces. Coordinate space uses three coordinates. Instead of an ordered pair, an ordered triple is used. The new variable, z, measures the distance forwards or backwards that you move. The ordered triple looks like this: (x, y, z). You might see more on space and 3-D figures later, in a different section.

- Jaime III
"Give me a fruitful error anytime, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself." - Vilfredo Pareto