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∘ left. From there, Andy moves 2 units (north) and then turns 90∘ left. He then moves 3 units (west) and again turns 90∘ left. Andy continues this process, increasing his distance each time by 1 unit and always turning left. What is the location of the point at which Andy makes the 2020th left turn?
Answer Choices:
A. (−1030,−994)
B. (−1030,−990)
C. (−1026,−994)
D. (−1026,−990)
E. (−1022,−994)
Solution:
Andy makes a total of 2020 moves: 1010 horizontal (505 left and 505 right) and 1010 vertical (505 up and 505 down). The x-coordinate of Andy's final position is
You can find that every four moves both coordinates decrease by 2. Therefore, both coordinates need to decrease by two 505 times. You subtract, giving you the answer of (B)(−1030,−990).