Post a New Question | Current Questions | Live Experts | Download
Homework Help: Math: Geometry: Lines
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.
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 shown by putting the letter A next to the letter B, and drawing one straight line over the two with arrows pointing outward at the ends. 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 shown by putting the letter A next to the letter B with one straight line over the two. 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 shown by writing the letter A next to the letter B, and one straight line over the two with only one arrow at one of the points.
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. In space, vertical lines never meet (they just go straight up or 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.
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. Perpendicular lines are lines that intersect in one point and form a 90 degree angle while they're at it. 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.
Homework Help: Math: Geometry
For Further Reading
|
