some points on a plane are marked and they are connected pairwise by line segments.if the total number of line segments formed is 10,find the number of marked points on the plane.
Answers
Given : some points on a plane are marked and they are connected pairwise by line segments. total number of line segments formed is 10
To find : the number of marked points on the plane.
Solution:
Let say points marked on plane = n
To Form a line segment we need 2 points
Hence number of ways two points can be selected
= ⁿC₂
( as order does not matter her as Line segment AB & BA are same )
ⁿC₂ = n(n-1)/2
n(n-1)/2 = 10
=> n² - n = 20
=> n² - n - 20 = 0
=> n² - 5n + 4n - 20 = 0
=> n(n - 5) + 4(n - 5) = 0
=> (n + 4) (n - 5) = 0
=> n = 5 , n = - 4 ( points can not be negative )
Hence the number of marked points on the plane = 5
Learn More:
Some points are plotted onplotted on a plane such that any three of ...
https://brainly.in/question/13996891
4. A line segment gets divided by the point(2k - Brainly.in
https://brainly.in/question/15136516