Use the three approaches of direct deductive reasoning to find the maximum number of points of intersection determined by n coplanar lines. Notice that 4 lines determine a maximum number of 6 points on intersection. Explain why the process is correct. Draw the nth diagram as shown in the class notes. Name each approach used. 41 12 13

In the solution, include a complete description and use of variables, a drawing of the nth diagram, and an explanation of why the process works. I need to use the three strategies of deductive reasoning below. 

Strategy 1: Repeating objects (e.g., points of intersection)

Strategy 2: No repeating objects (e.g., points of intersection)

Strategy 3: Inductive-deductive reasoning