Question

If you place 35 points on a piece of paper so that no three points are in a line, how many line segments are necessary to connect each point to all the others?

Answer 1

595 line segments are necessary to connect each point to all the others.

Explanation:

Consider the provided information.

The formula for the number of line segments between "n" non-collinear points is:

`(n* ( n -1 ))/(2)` Segments

Here it is given that there are 35 points.

Substitute n = 35 in above formula.

`(35* (35 -1 ))/(2)`

`(35* 34)/(2)`

`35* 17`

`595` Segments

Hence, 595 line segments are necessary to connect each point to all the others.