Question 6. Mona wants to draw the figure shown without lifting her pencil from the paper. The lengths of the three segments are given. What is the shortest total length she could draw? Mona has two reasonable types of locations she can start at. She can either start at the outside end of a line segment, or she can start in the center. If she starts in the center of a segment, after she draws to one end, she will have to backtrack over the already drawn line to draw the other part of the segment. Let's first look at what happens if she starts in the center. After she draws a segment, she is unable to directly go to the next segment. She must first backtrack to the center before she can draw her next line segment. Now let's look at what happens if Mona starts on the edge. We can see that after she draws a segment, she ends up in the center and can directly draw the next segment, which means she draws less than the blue example, but still reaches the same point. Since Mona is in the center now, as shown by our blue example from earlier, she must backtrack over a line before proceeding to the last segment. The best option would be to backtrack over the shortest segment, like how it is shown in our diagram. This gives us a distance of 3 cm, plus 1 cm, plus 1 cm, plus 2 cm, which equals 7 cm.

drawing strategy

minimize length

pencil drawing

segment backtrack

efficient path