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## Main Question or Discussion Point

The original problem for anyone that can read Chinese:

https://zerojudge.tw/ShowProblem?problemid=b221

The problem defines a convex polygon with multiple points located in the first quadrant and the required task is to find a linear function y = ax that can spilt the polygon into two parts each with the same area.(The “a” can be within the accuracy of 0.02 from the actual answer,see why in a second)

Since this is actually a program question (Like the ones on Project Euler or UVa) so I originally wrote a program that basically tries every possible a value from y-axis to x-axis(via survey formula),but my program fail to finish in the time limit,so I think this problem may require some math insight which I don’t have.

Are there any suggestions on how this might have been done?Since it leaves a space for error,does it has something to do with calculus?

https://zerojudge.tw/ShowProblem?problemid=b221

The problem defines a convex polygon with multiple points located in the first quadrant and the required task is to find a linear function y = ax that can spilt the polygon into two parts each with the same area.(The “a” can be within the accuracy of 0.02 from the actual answer,see why in a second)

Since this is actually a program question (Like the ones on Project Euler or UVa) so I originally wrote a program that basically tries every possible a value from y-axis to x-axis(via survey formula),but my program fail to finish in the time limit,so I think this problem may require some math insight which I don’t have.

Are there any suggestions on how this might have been done?Since it leaves a space for error,does it has something to do with calculus?