A Bug's Journey

[From the Fourth Annual Iowa Collegiate Mathematics Competition. Written by Paul Zeitz. Slight modifications by Sam Rebelsky.]

A bug is crawling on the coordinate plane from )7,11) to (-17,3). The bug travels at a constant speed of one unit per second everywhere but in quadrant II (with negative x coordinates and positive y coordinates), where it travels at 1/2 units per second. What path should the bug take to complete its journey in minimal time.

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