Question

Some points are plotted on a plane. Each point joined with all remaining points by line segments.

Find the number of points if the number of line segments are 10.​

Answer 1

Answer:

27

Step-by-step explanation:

Total number of points = 10

Number of points that are not collinear =

3

Taking any 10 points in a plane - A, B,C,D,E,F,G,H,1,J.

Since, 4 of these points are joined to 6 of the remaining points, we will divide the 10 points into two groups containing 4 and 6 points.

Let the first group be A, B, C, D and the second group contains the remaining 6 points EFGHIJ.Thus each point in first group is joined to each point in the second group.

Line segments formed - 6+6+6+6 =24. (As A is joined to 6 points, B is joined to 6 points and so on)

Each point from the group of 6 is joined to 5 other points. Let these 6 points be already connected to 4 points in other group, then it is required to connect each point to 1 more point from the same group, hence dividing these group of sixinto 3 groups of 2 and each group of 2 forming one line segment.

Segments formed 24+3 = 27

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