Problem

2020 AMC 10B Problem 13

Andy the Ant lives on a coordinate plane and is currently at (-20, 20) facing east (that is, in the positive x-direction). Andy moves 1 unit and then turns 90^{\circ} left. From there, Andy moves 2 units (north) and then turns 90^{\circ} left. He then moves 3 units (west) and again turns 90^{\circ} left. Andy continues his progress, increasing his distance each time by 1 unit and always turning left. What is the location of the point which Andy makes the 2020 left turn?

\textbf{(A)}\ (-1030, -994)\qquad\textbf{(B)}\ (-1030, -990)\qquad\textbf{(C)}\ (-1026, -994)\qquad\textbf{(D)}\ (-1026, -990)

\textbf{(E)}\ (-1022, -994)


Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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Problem Tags: 2-d Game theory Geometry

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