A ‘plane’ (e.g. the Cartesian plane) is a fl at surface like the top of the desk, or the teacher’s board, except that it goes on and on forever in every direction.
A word we use for ‘going on forever’ is infi nity, and the symbol for infi nity is ∞ . A plane is a fl at surface that goes on forever in every direction.
Discuss and discover
(i) Make a list of what you already know about lines. (ii) Working in pairs, fi nd the minimum number of points you would need if you want to construct (draw) a line.
(iii) How did you solve this problem? (iv) How can you be sure you have found the minimum number of points?
Line
A point is an exact location in a space or on a plane. A point is represented by an italic uppercase letter.
There is exactly one straight line through any two points.
A B We denote (represent) a line as AB or BA.
The arrows indicate that the line extends to infi nity ( ∞ ) in both directions. Ray
A ray is a line that starts at one point and continues to infi nity in one direction.
A
The notation used to describe the distance between points A and B is |AB| or |BA| .
B
The image above shows a ray that starts at A and goes through point B and extends to infi nity ( ∞ ). This ray is denoted by [AB. The square bracket shows there is one endpoint and it extends to infi nity in the opposite direction.
The arrow at the end shows that the ray continues to infi nity in that direction.
If point C lies on the line segment between point A and point B , then |AB| = |AC| + |CB| A
C B
Line segment A line segment is a part of a line. It has two end points. A
B
A line segment is denoted by [AB] or [BA]. The square brackets show there are two endpoints.
A line segment is the shortest distance between two points. It has a fi xed length, so there are no arrows at the ends.
A line segment is always a straight line.
Length of a line segment The length of a line segment is the distance between the two end points of a line segment.
A B The distance from A to B is equal to the distance from B to A. plane
Section A Introducing concepts and building skills