Difference between revisions of "2020 AMC 10B Problems/Problem 13"
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== Solution 1 == | == Solution 1 == | ||
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Andy makes a total of <math>2020</math> moves: <math>1010</math> horizontal (<math>505</math> left and <math>505</math> right) and <math>1010</math> vertical (<math>505</math> up and <math>505</math> down). | Andy makes a total of <math>2020</math> moves: <math>1010</math> horizontal (<math>505</math> left and <math>505</math> right) and <math>1010</math> vertical (<math>505</math> up and <math>505</math> down). | ||
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~MRENTHUSIASM | ~MRENTHUSIASM | ||
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+ | == Solution 2 == | ||
+ | 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 <math>\boxed{\textbf{(B)}\ (-1030, -990)}.</math> | ||
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+ | ~happykeeper | ||
== Video Solution == | == Video Solution == |
Revision as of 16:38, 8 September 2021
Problem
Andy the Ant lives on a coordinate plane and is currently at facing east (that is, in the positive
-direction). Andy moves
unit and then turns
degrees left. From there, Andy moves
units (north) and then turns
degrees left. He then moves
units (west) and again turns
degrees left. Andy continues his progress, increasing his distance each time by
unit and always turning left. What is the location of the point at which Andy makes the
th left turn?
Solution 1
Andy makes a total of moves:
horizontal (
left and
right) and
vertical (
up and
down).
The -coordinate of Andy's final position is
The
-coordinate of Andy's final position is
Together, we have
~MRENTHUSIASM
Solution 2
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
~happykeeper
Video Solution
~IceMatrix
Similar Problem
2015 AMC 10B Problem 24 https://artofproblemsolving.com/wiki/index.php/2015_AMC_10B_Problems/Problem_24
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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