Chapter 1, Problem 42RP

a

To determine

To calculate: The maximum number of lines determined in the paper are to be found

Answer to Problem 42RP

The number of lines formed is $21$

Explanation of Solution

Given information: The following information is given in the question

• Any four of them are non colinear
• No three of them are colinear − we will assume for maximum lines to be determined

Formula used: Number of lines formed by n points with no three of them colinear

  $lines=\frac{n(n+1)}{2}$

Calculation: We will work on the above equation with $n=6$ to find our answer

Substituting $n=6$ , we get

  $lines=\frac{6(7)}{2}=21$

Thus, the number of lines formed is $21$

b

To determine

To calculate: The minimum number of lines determined in the paper are to be found

Answer to Problem 42RP

The number of lines formed is $2$

Explanation of Solution

Given information: The following information is given in the question

• Any four of them are non colinear
• Two sets of three are colinear − we will assume for minimum lines to be determined

Formula used: Logical reasoning is used

Calculation: Using the above statements, we can see that for two sets of colinear points, we will have only two non colinear lines

Thus, the number of lines formed is $2$