Minimum Distance between 2 points

[mathdaemon]

Hello

10 points are randomly selected in a square with each side 3 units. Then there will be atleast 2 points(out of the 10) such that the distance between them does not exceed
a)1 b)sqrt(2) c)sqrt(2-1) d) 2-sqr(2)

7 points were randomly selected in a regular hexagon with side 1 unit. There will be atleast 2 points(out of the 10) such that the distance between them does not exceed
a)1 b)sqrt(2) c)sqrt(2-1) d) 2-sqr(2)

I have SOLVED one such problem in which it was required to find minimum distance between 2 points(out of 5) in a unit length equilateral triangl
but I am not able to solve the above problems.
Please help.

Thanks

 

[Deleted member 4993]

Hello

10 points are randomly selected in a square with each side 3 units. Then there will be atleast 2 points(out of the 10) such that the distance between them does not exceed
a)1 b)sqrt(2) c)sqrt(2-1) d) 2-sqr(2)

7 points were randomly selected in a regular hexagon with side 1 unit. There will be atleast 2 points(out of the 10) such that the distance between them does not exceed
a)1 b)sqrt(2) c)sqrt(2-1) d) 2-sqr(2)

I have SOLVED one such problem in which it was required to find minimum distance between 2 points(out of 5) in a unit length equilateral triangl
but I am not able to solve the above problems.
Please help.

Thanks

What is the largest distance between two vertices of a square (side = a)?

What is the largest distance between two vertices of a regular hexagon (side = a)?

 

[Ishuda]

Hello

10 points are randomly selected in a square with each side 3 units. Then there will be atleast 2 points(out of the 10) such that the distance between them does not exceed
a)1 b)sqrt(2) c)sqrt(2-1) d) 2-sqr(2)

7 points were randomly selected in a regular hexagon with side 1 unit. There will be atleast 2 points(out of the 10) such that the distance between them does not exceed
a)1 b)sqrt(2) c)sqrt(2-1) d) 2-sqr(2)

I have SOLVED one such problem in which it was required to find minimum distance between 2 points(out of 5) in a unit length equilateral triangl
but I am not able to solve the above problems.
Please help.

Thanks

Taking the first problem, are the points picked randomly all inside one 3X3 square or are they picked to be inside one of the nine 1X1 unit squares? From the different choices of answers, it appears to be inside one of the nine 1X1 squares. If that is the case, consider the fact that there is more points that the number of squares and what that means. Also what is the maximum possible distance between two points in a unit square.

The same sort of reasoning applies to problem two.

 

[mathdaemon]

Hi

Thanks for the answers I solved the square related question but I am unable to make any progress in the regular hexagon problem. Some more hints would be appreciated.

Thanks again

 

[Ishuda]

Hi

Thanks for the answers I solved the square related question but I am unable to make any progress in the regular hexagon problem. Some more hints would be appreciated.

Thanks again

Consider the properties of a regular hexagon, especially in view of your statement about equilateral triangle.