2023 AMC 12B Problems/Problem 9
Revision as of 20:40, 15 November 2023 by Pi is 3.14 (talk | contribs)
- The following problem is from both the 2023 AMC 10B #13 and 2023 AMC 12B #9, so both problems redirect to this page.
Problem
What is the area of the region in the coordinate plane defined by
?
Solution
First consider, We can see that it's a square with radius 1 (diagonal 2). The area of the square is
Next, we add one more absolute value and get This will double the square reflecting over x-axis.
So now we got 2 squares.
Finally, we add one more absolute value and get This will double the squares reflecting over y-axis.
In the end, we got 4 squares. The total area is
~Technodoggo ~Minor formatting change: e_is_2.71828
Video Solution 1 by OmegaLearn
See Also
2023 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 |
2023 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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 12 Problems and Solutions |
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