Difference between revisions of "2014 AMC 10A Problems/Problem 18"
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Note that the difference in <math>y</math> value of <math>B</math> and <math>C</math> is <math>4</math>. By rotational symmetry of the square, the difference in <math>x</math> value of <math>A</math> and <math>B</math> is also <math>4</math>. Note that the difference in <math>y</math> value of <math>A</math> and <math>B</math> is <math>1</math>. We now know that <math>AB</math>, the side length of the square, is equal to <math>\sqrt{1^2+4^2}=\sqrt{17}</math>, so the area is <math>\boxed{\textbf{(B) }17}</math>. | Note that the difference in <math>y</math> value of <math>B</math> and <math>C</math> is <math>4</math>. By rotational symmetry of the square, the difference in <math>x</math> value of <math>A</math> and <math>B</math> is also <math>4</math>. Note that the difference in <math>y</math> value of <math>A</math> and <math>B</math> is <math>1</math>. We now know that <math>AB</math>, the side length of the square, is equal to <math>\sqrt{1^2+4^2}=\sqrt{17}</math>, so the area is <math>\boxed{\textbf{(B) }17}</math>. | ||
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+ | === Video Solution=== | ||
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+ | https://www.youtube.com/watch?v=iPPQUrNE4RE | ||
+ | |||
+ | ~ naren_pr | ||
==See Also== | ==See Also== |
Latest revision as of 10:37, 1 March 2021
Contents
Problem
A square in the coordinate plane has vertices whose -coordinates are , , , and . What is the area of the square?
Solution
Let the points be , , , and
Note that the difference in value of and is . By rotational symmetry of the square, the difference in value of and is also . Note that the difference in value of and is . We now know that , the side length of the square, is equal to , so the area is .
Video Solution
https://www.youtube.com/watch?v=iPPQUrNE4RE
~ naren_pr
See Also
2014 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.