Question

Consider a set of 9 ponts in coordinate plane say ((1,1),(-1,-1),(1,-1),(-1,1),(0,1),(0,-1),(1,0),(-1,0),(0,0)) ,number of distinct lines that pass through at least two points from this set is

Answer 1

Answer with explanation:

To draw a distinct line you need at least two points in Two or three dimensional coordinate plane or in space.

If the set of nine points in the Space or plane are Col linear , there will be a single line passing through all these points.

Plotting the set of nine points in two dimensional plane

There are 8 lines ,which will pass through 3 points.

To find number of line passing through 2 points we will apply the rule of combinatorics.

From 9 points , number of  lines,  passing through, 2 points

$_{2}^{9}\textrm{C}=\frac{9!}{2! \times (9-2)!}$

$=\frac{9!}{7! \times 2!}\\\\=\frac{9 \times 8\times 7!}{7!\times 2!}\\\\=\frac{9\times 8}{2}=9\times 4=36$

So, number of distinct lines passing through 9, points out of  which, 8 lines are passing through 3 col linear points.

       =36-8

      =28

=28, distinct lines

Answer 2

So, number of distinct lines passing through 9, points out of which, 8 lines are passing through 3 col linear points.

=36-8

=28

=28, distinct lines