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take a triangle. Three straight lines are drawn through the vertices of the triangle as shown.The maximum number of points of intersection is 3.
Draw two lines through each vertex of a triangle to meet the opposite sides. What is the maximumnumber of points of intersection.
Find again drawing the maximum number of points of intersection when three lines are drawn through each vertex.
Without drawing can you guess the maximum points of intersection for 4 lines ?
Correct Answer: 48
Drawing 1 line through each vertex gives a maximum of 3 intersection points, drawing 2 lines through each vertex gives 12, and drawing 3 lines through each vertex gives 27. These values follow the pattern $$3n^2$$ for n lines through each vertex, since $$3\times 1^2=3$$, $$3\times 2^2=12$$, $$3\times 3^2=27$$. Following the same pattern, for 4 lines the maximum number of points of intersection is $$3\times 4^2=48$$.
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