Any1 know geometry?

Question

Ok, here is the question in my geometry I hope to get good answers:
Sketch six points A,B,C,D,E and F, no three of which are collinear. Name the lines defined by these points. How many lines are there? Please show work

Answer 1

Hi,

If you have 6 non collinear points, you could start at any of 6 points. A line could then be drawn to any of the remaining 5 points. That would make 6 x 5 or 30 lines, BUT drawing from point A to B would be the same as drawing from B to A, so there are actually half as many or 30/2 or 15 lines possible.

( The first answer correctly told you there would be 9 diagonals, but forgot about the 6 lines through the points around the outside.)

I hope that helps!! :-)

Answer 2

AB AC AD AE AF
BC BD BE BF
CD CE CF
DE DF
EF
5 + 4 + 3 + 2 + 1 = 15
This is all the possible combinations of 6 things taken 2 at a time. This is also an arithmetic series. The general formula for N points is N(N-1)/2.

Answer 3

Just draw a regular hexagon. Then draw all the diagonals.
The number is d = n(n-3)/2 = 6(6-3)/2 = 9