A bug wants to travel from the point (7,11) to the point (-17,-3). At quadrant II, the speed of the bug is 1/2 unit per second but everywhere else, its speed is 1 unit per second. What path should the bug take to minimize the travelling time?

Question

anonymous · Answer

help plz!!!!

nory · Answer

If you write an equation relating the bug's path and the time, you can minimize the time using calculus. I can't think of such an equation, but I think this is the right path.

anonymous · Answer

yea i know the answer, the answer was to connect the point to the origin then connect the origin to the other point
but i needed a proof on how to determine that this path is the shortest time
ive gotten a hint was to use symmetry but im not sure on how to use it to proove the problem