Question

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. Three
B. Four
C. Five
D. Six

Answer 1

6

Explanation:

possible points are:

ad

ac

ab

dc

db

cb

Answer 2

Option D 6 is the answer.

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 segments

AB, AC, AD, BC, BD, DC

Therefore 6 segments can be formed.

(2) By combination method

Number of segments =
`^(4)C_(2)`

=
`(4!)/(2!2!)=(4* 3* 2* 1)/((2* 1)* (2* 1))`

=
`(4* 3)/(2* 3)=(12)/(2)`

= 6

Option D 6 is the answer.