What is the Point ?
A point is represented as a dot, which denotes a very specific location. It has no dimensions, i.e. no width, length, or depth.
What is a Line and a Line Segment?
When two points are joined by a straight line you get a line segment, when it is extended indefinitely on both ends which is represented by arrows at both ends, we get a line. It has no beginning and no end in both directions (infinite). A line is one-dimensional.
Line AB
Line segment TS
What is a Ray?
A ray has two points joined by a straight line segment. But at one point the line extends indefinitely and at the other point it does not. Hence, rays extend only in one direction.
When naming a ray, it is shown by putting a little ray symbol on the top of the two points and the arrow depicts the direction in which the ray extends. For example:
Types of Lines
(1) Intersecting lines :
Intersecting lines are formed when any two lines cross each other. The point of intersection is a common point that exists on both intersecting lines. Intersecting lines meet at one point.
Lines AB and CD intersect at point P.
(2) Parallel lines:
Parallel lines are defined as two or more lines that reside in the same plane but never intersect. The corresponding points at these lines are at a constant distance from each other.
The above lines are parallel. They are at a constant distance from each other. They never intersect with each other.
Parallel lines are denoted by the symbol ||.
EF And HG are parallel lines. It is written as EF||GH.
(3) Perpendicular lines:
Perpendicular lines are two intersecting lines that intersect at 90 degrees.
The sign ⟂ is used to symbolise that two lines are perpendicular. The symbol means “is perpendicular to”.
In the given figure AB is perpendicular to CD or AB ⟂ CD.
Solved Examples on Rays, Lines, Line Segment & Points
Example 1:
Answer:
Example 2: A line RQ is parallel to the line PS and another line intersects both lines at A and B points, but the intersecting line is not perpendicular to the other two lines. Draw and label the diagram.
Answer:
PS and QR are parallel and a line intersects PS at B and RQ at A such that the intersecting line AB is not perpendicular to lines PS and RQ.
Example 3: Observe the figure given below and identify or name:
Solution:
a. A point is represented as a dot. Hence, the points in the given figure are A, B, C, D, E and F.
b. The points B, D are joined by a straight line so that you get a line segment \(\overline{\text{BD}}\).
The points B, F are joined by a straight line so that you get a line segment \(\overline{\text{BF}}\).
c. The two points B, E joined by a straight line segment which is extended at one side forms a ray BE.
The two points B, C joined by a straight line segment which is extended at one side forms a ray BC.
The two points B, A joined by a straight line segment which is extended at one side forms a ray BA.
d. A line AC is extended indefinitely on both ends which are represented by arrows at both ends, hence we get a line.
Example 4: Observe the figure given below and identify or name:
Solution:
a. A point is represented as a dot. The line that contains the point Q is ST.
b. The two points Q, T joined by a straight line segment forms a ray QT. From the figure the end point of the ray QT is Q.
c. The two opposite rays are ray QT and ray QS.
Example 5: There are different roadways between each pair of cities on the map. Can you draw a way using line segments to represent the travel starting from Oswego and back to Oswego through Rochester, Buffalo, Endicott and Syracuse?
Solution:
One way to represent the journey, we draw a:
- Line segment from Oswego to Rochester.
- Line segment from Rochester to Buffalo.
- Line segment from Buffalo to Endicott.
- Line segment from Endicott to Syracuse.
- Line segment from Syracuse to Oswego.
A pair of opposite rays are two rays that extend in opposite directions and have the same endpoint. As a result, a pair of opposite rays always form a line. Hence two rays can form a line.
Perpendicular lines are formed when two lines intersect at 90 degrees. Therefore, all perpendicular lines are intersecting lines. But all intersecting lines are not perpendicular.