Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Let n = the number of points
(x-1) + ... (x-x)
The last term will always be 0, when you reach that, stop.
ex. 1pt: 1-1=0
2pt: (2-1) + (2-2) = 1
3pt: (3-1) + (3-2) + (3-3) = 3
(x-1) + ... (x-x)
The last term will always be 0, when you reach that, stop.
ex. 1pt: 1-1=0
2pt: (2-1) + (2-2) = 1
3pt: (3-1) + (3-2) + (3-3) = 3
⇒Number of Points in the Plane = n
→There are two Possibility
Either All Points are Collinear, that is Lie Along a Line.
Or, They are, Non- Collinear.
To Determine a segment we need two distinct points.
If All "n" Points are Collinear,Distinct Number of Segment=1
If there are two points in plane, number of Distinct Segment
[tex]=_{2}^{2}\textrm{C}\\\\=\frac{2!}{(2-2)! \times 2!}\\\\=1[/tex]
If there are three points in plane, number of Distinct Segment
[tex]=_{2}^{3}\textrm{C}\\\\=\frac{3!}{(3-2)! \times 2!}\\\\=3[/tex]
If there are Four points in plane, number of Distinct Segment
[tex]=_{2}^{4}\textrm{C}\\\\=\frac{4!}{(4-2)! \times 2!}\\\\=6[/tex]
............................................................................................
..................................................................................
⇒So,If Points are Not Collinear,that is there are "n" points in the plane, then Distinct number of Segment
[tex]=_{2}^{n}\textrm{C}\\\\=\frac{n!}{2!\times (n-2)!}\\\\=\frac{n \times(n-1)}{2}[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
