Question

There are 4 points on a plane in the following situation how many straight line can be constructed? Explain your answer by drawing suitable diagram.
A) All the points are collinear
B)out of the four, any three are non - collinear​

Answer 1

Given:

A plane with four points in it.

To find: How many straight lines can be drawn using those four points in the given conditions:

• All the points are collinear.
• Out of four, any three are non - collinear.

Collinear: Any two points are said to be collinear, if they lie on the same line. And, vice- versa.

Note: For the explanation, images with the given conditions are attached to the solution. Image with name Plane1 is for the first condition and image with the name Plane2 is for the second condition.

Answer:

Considering the given conditions,

A) All the points are collinear: This statement means that all the given points are on the single imaginary straight line.

• In the image attached (Name: Plane1), the figure "1" illustrates the first condition "all points collinear".
• Let the points be denoted as A, B, C, D.
• Now, try to join the four points in different ways.
• This can be seen in the image (Plane1) and the different possible ways are named as (a), (b), (c) and (d).
• (a)- In this, one line is constructed by joining the points A and B.
• (b)- In this, one line is constructed by joining the points B and C.
• (c)- In this, one line is constructed by joining the points C and D.
• (d)- In this , one line is constructed by joining all the four points A, B, C and D.
• Hence, from the figure, it can be seen that only four lines can be constructed using the four points, if all the four points are collinear.

B) Out of four, any three are non-collinear: This statement implies that any two points can be in a straight line.

• An image with name "Plane2" is attached to illustrate this condition.
• From the image, the main figure numbered as "2", shows the plane with four points A, B, C and D out of which any two points are collinear.
• Right side of the image shows the different ways in which, the four points can be joined to construct lines.
• (a) - In this, one line is constructed by joining the points A and B.

• (b) - In this, one line is constructed by joining the points B and C.

• (c) - In this, one line is constructed by joining the points C and D.

• (d) - In this, one line is constructed by joining the points D and A.

• (e) - In this, one line is constructed by joining the points A and C.

• (f) - In this, one line is constructed by joining the points D and B.
• This shows that, using the given points, six lines can be constructed in this case.