Lines from Seven Points

Difficulty: Medium · Topics: Discrete Mathematics, Combinations, Geometry

Points A, B, C, D lie on one line and E, F, G on another.

graph "x":[-2.2,5.0],"y":[-1.0,4.6],"axes":false,"ink":true,"label":"Points A, B, C, D on one line and E, F, G on another line","items":["type":"line","from":[0.6,4.2],"to":[-1.4,-0.6],"type":"line","from":[2.0,3.6],"to":[4.2,-0.6],"type":"point","at":[0.44,3.816],"label":"A","anchor":"w","type":"point","at":[-0.04,2.664],"label":"B","anchor":"w","type":"point","at":[-0.5,1.56],"label":"C","anchor":"w","type":"point","at":[-0.96,0.456],"label":"D","anchor":"w","type":"point","at":[2.264,3.096],"label":"E","anchor":"e","type":"point","at":[2.924,1.836],"label":"F","anchor":"e","type":"point","at":[3.54,0.66],"label":"G","anchor":"e"]

At most how many different lines can be drawn through these 7 points?