THe maximum number of lines that can be achieved between 9 points is 8+7+6+5+4+3+2+1=36.
parrellell
a nonagon
Groups are 11, 12, 1, 2; 3, 4, 9 and 10; 5, 6, 7 and 8 so you draw your lines: from between 2 and 3 to between 10 and 11 and from between 4 and 5 to between 8 and 9.
Points: (-2, 7) and (3, 6) the slope is -1/5 Points: (4, 2) and (9, 1) the slope is -1/5 Both slopes are the same and so therefore they are parallel lines
I get 9 triangle with fewer than 9 lines. Draw a square: ABCD (4 lines) Draw the diagonals AC, BD (2 lines) which meet at X in the centre. On a separate part of the page, draw triangle PQR (3 lines). That is 4 + 2 + 3 = 9 lines. The triangles are: ABC, BCD, CDA, DAB, AXB, BXC, CXD, DXA, and PQR 9 triangles with 9 lines. Could have done 13 triangles with 7 lines by drawing a line from A to BC.
parrell
T E N (count the lines: 2 in T, 4 in E, and 3 in N = 9 lines)
They are intersecting lines.
perpendicular
Draw a clock face. Draw lines between 12:00 to 5:00, 4:00 to 9:00 and 1:00 to 8:00.
THe maximum number of lines that can be achieved between 9 points is 8+7+6+5+4+3+2+1=36.
I'll do my best to illustrate it here * * • • • • • * • • * Start at the top left star, and draw a line to the bottom right star. Then go to the star all the way above that one. Draw a diagonal to the bottom left star, and draw a line left until you get to the center bottom dot. Tada!
draw lines and connect them
9
parrellell
a nonagon