2020 AMC 10B Problems/Problem 13

Problem

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 $90^{\circ}$ degrees left. From there, Andy moves $2$ units (north) and then turns $90^{\circ}$ degrees left. He then moves $3$ units (west) and again turns $90^{\circ}$ degrees left. Andy continues his progress, increasing his distance each time by $1$ unit and always turning left. What is the location of the point at which Andy makes the $2020$ th left turn? $\textbf{(A)}\ (-1030, -994)\qquad\textbf{(B)}\ (-1030, -990)\qquad\textbf{(C)}\ (-1026, -994)\qquad\textbf{(D)}\ (-1026, -990)\qquad\textbf{(E)}\ (-1022, -994)$

Solution 1

You can find that every four moves both coordinates decrease by 2. Therefore, both coordinates need to decrease by 2 505 times. You subtract, giving you $\boxed{\textbf{(B) } \text{(-1020,-990)}}$

Video Solution

https://youtu.be/t6yjfKXpwDs

~IceMatrix

2020 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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2020 AMC 10B Problems/Problem 13

Contents

Problem

Solution 1

Video Solution

See Also