Question

What do you mean by collinear points?
Given three collinear points A, B, C. How many line segments do they determine? Name them.

Answer 1

Hint: Understand the definition of collinear points by considering three points in a plane or space. Now, consider the given figure and write the name of available line segments by using the definition of line segment which says that “a line segment has two endpoints”.

Complete step-by-step answer:
Here, we have been asked to define collinear points.
In geometry, the collinear points are defined as a set of points that lie on a single line. This property of a set of points lying on a single line is called collinearity of the set of points. Now, for the term collinear points to be defined we must have three points because two points are always collinear and for a single point the term collinear is undefined.
Now, if we are given any set of points, for example: - a set of three points P, Q and R and we have to check if they are collinear or not, then we will try to draw a single straight line passing through all three of them. If we are able to draw this single line then the three points will be collinear otherwise not. Let us consider these examples: -
1.

Here, we can see that we are able to draw a single straight line through three points P, Q and R, so they are collinear in nature.
2.

Here, in this case we cannot draw a straight line through P, Q and R so they are not collinear.
Now, let us come to the second part of the question. Here, we have been given three collinear points A, B and C and we have been asked to write the names of all line segments formed. First let us see the definition of ‘line segment’.
In geometry, a line segment is a part of a line that is bounded by two distinct endpoints. For example: -

The above figure represents a line segment containing two end points X and Y.
Now, in the question we have been given the figure shown below,

Here, we can see three lines namely AB, BC and AC. Line segment AB contains two endpoints, A and b. Line segment BC contains two endpoints, B and C. Line segment AC contains two endpoints, A and C.

Note: One may note that without understanding the definition and properties of collinear points and line segments, we cannot solve the above question. You must remember the definitions of basic geometry elements like points, line segments, lines etc. The difference between a line, a ray and a line segment must be known so that you may not get confused. Remember that a line has no end point, a ray has one endpoint and a line segment has two endpoints.