Direction problem

The answer is E.
The solution can be well understood if you can draw the directions where P moves from start point.

Well, though I have applied simple logic I don't have a concrete formula or mathematical solution!

As you can see, p first walks Right then goes down South then again moves up in the east direction for 2828 then in the direction of p but surpasses it and goes 4242
the difference between 4242 and 2828(4242+2828= 7000; and the 2000 east and 4000(2000+4000=6000) south is 1000 steps.

Hence, E.

IMO 5

I tried substituting the numbers in terms of 2000
(i.e. walked x feet east, than 2x south, than roughly 1.5x northeast, so on and so on) but I couldn't really get a clear cut answer. I believe this is a geomotry question, I just wish I had sharper skills in that category.

Just drawing this out, it looks like the person is definitely North east of Point P, but I don't know the exact distance. This looks like a trick question. I may be wrong, but when my first gut jumps at an answer after little to no work, I can almost guarentee that its the wrong answer.

I tried numerous approaches
First I looked at the answers
Only the directions N, E, W, and NE are given (or at point P)
Since South is not taken into account, I disgard the 4000 steps the person went down south.
1 way I did this was I add East vs. West.
2000 + 2828 - 4242 - 1414 = 828. He's about 1,000 steps West of Point P using that approach.

Good question. Would love to see other's approach on this