Question

number of common points in two non parallel lines ​

Answer 1

Answer:

One line, no intersections.

Two lines, one intersection.

Three lines, three intersections.

Four lines, six intersections.

There appears to be a pattern emerging. 1,3,6 are the first three triangular numbers.

Triangular numbers are the sum of the numbers from 1 to n and are a special case of the sum of an arithmetic series which is equal to

n(n+1)2n(n+1)2

As the nthnth new line is added it crosses all the (n−1)(n−1) lines laid down before it adding (n−1)(n−1) intersections to the total creating the (n−1)th(n−1)th triangular number.

So for nn lines the number of intersections is:

n(n−1)2n(n−1)2

This must be viewed as the maximum possible number of intersections, as it is possible that an intersection is used by more than two lines.

y=x,y=−xy=x,y=−x and y=2xy=2x are all non-parallel but pass through the origin 0,00,0

Step-by-step explanation:

Hope this helps you