Lines are more related to geometry than to math and could be considered as under math lines. Therefore if the above title was ‘geometry lines’, also it would have been apt.
What are lines?
A line is a set of points that has only one dimension, length.
A line AB is shown in the given diagram. The arrow heads on the line AB show that it is extending endlessly in both the directions and has no end points. Hence a line has no fixed length. Or we can say that the length of a line is infinite. We used the two points A and B to define the line. Therefore in general we can say that two distinct points in a plane determine a line. In other words, if there is only one point under consideration, then there can be infinitely many lines passing through that point as shown in the figure below:
However if we have two points to describe a line, then there can be only one line that passes through both these points.
In co-ordinate geometry, a line can be defined as a set of ordered pairs with a definite property. For example, if we have an ordered pair (x,y) such that y = 2x + 1, that means that all those values of x and y that satisfy the above equation, would be a part of the line defined by that equation.
Some special subsets of a line:
1. Line segment: A line segment is simply a part of a line that has a specific length and specific end points as shown in the diagram below:
Here CD and PN are both line segments. Note that the end points are dots and not arrows as was the case with line.
2. Ray: A ray is a part of a line that has only one end point. It extends endlessly in one direction. See figure below:
In the above figure AF is a ray. It has one end point at A and extends endlessly in the other direction. Therefore it has a dot at one end and an arrow at the other end.
Two lines can be related to each other in four different ways:
1. Lines that have just one point in common are called intersecting lines.
2. Lines that lie the same plane but never intersect even if produced endlessly in both directions are called parallel lines.
3. Two intersecting lines that form a right angle are called perpendicular lines.
4. Lines that are not in the same plane and do not intersect are called skewed lines.
What are lines?
A line is a set of points that has only one dimension, length.
A line AB is shown in the given diagram. The arrow heads on the line AB show that it is extending endlessly in both the directions and has no end points. Hence a line has no fixed length. Or we can say that the length of a line is infinite. We used the two points A and B to define the line. Therefore in general we can say that two distinct points in a plane determine a line. In other words, if there is only one point under consideration, then there can be infinitely many lines passing through that point as shown in the figure below:
However if we have two points to describe a line, then there can be only one line that passes through both these points.
In co-ordinate geometry, a line can be defined as a set of ordered pairs with a definite property. For example, if we have an ordered pair (x,y) such that y = 2x + 1, that means that all those values of x and y that satisfy the above equation, would be a part of the line defined by that equation.
Some special subsets of a line:
1. Line segment: A line segment is simply a part of a line that has a specific length and specific end points as shown in the diagram below:
Here CD and PN are both line segments. Note that the end points are dots and not arrows as was the case with line.
2. Ray: A ray is a part of a line that has only one end point. It extends endlessly in one direction. See figure below:
In the above figure AF is a ray. It has one end point at A and extends endlessly in the other direction. Therefore it has a dot at one end and an arrow at the other end.
Two lines can be related to each other in four different ways:
1. Lines that have just one point in common are called intersecting lines.
2. Lines that lie the same plane but never intersect even if produced endlessly in both directions are called parallel lines.
3. Two intersecting lines that form a right angle are called perpendicular lines.
4. Lines that are not in the same plane and do not intersect are called skewed lines.
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