MATH SOLVE

5 months ago

Q:
# If each point in the diagram can act as an endpoint, how many distinct line segments can be formed using the set of points A. ThreeB. FourC. FiveD. Six

Accepted Solution

A:

Answer:Option D 6 is the answer.Step-by-step explanation:the given points are A, D, C and B. If each point in the diagram can act as end points, we have to calculate number of distinct line segments formed.This ca be calculated in two ways.(1) We will form the line segmentsAB, AC, AD, BC, BD, DCTherefore 6 segments can be formed.(2) By combination methodNumber of segments = [tex]^{4}C_{2}[/tex]= [tex]\frac{4!}{2!2!}=\frac{4\times 3\times 2\times 1}{(2\times 1)\times (2\times 1)}[/tex]= [tex]\frac{4\times 3}{2\times 3}=\frac{12}{2}[/tex]= 6Option D 6 is the answer.