Difference between revisions of "2012 AMC 10B Problems/Problem 3"
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== Problem == | == Problem == | ||
− | The point in the <math>xy</math>-plane with coordinates (1000, 2012) is reflected across the line <math>y=2000</math>. What are the coordinates of the reflected point? | + | The point in the <math>xy</math>-plane with coordinates <math>(1000, 2012)</math> is reflected across the line <math>y=2000</math>. What are the coordinates of the reflected point? |
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math> | <math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math> |
Latest revision as of 13:23, 19 August 2017
Problem
The point in the -plane with coordinates is reflected across the line . What are the coordinates of the reflected point?
Solution
The line is a horizontal line located units beneath the point . When a point is reflected about a horizontal line, only the - coordinate will change. The - coordinate remains the same. Since the -coordinate of the point is units above the line of reflection, the new - coordinate will be . Thus, the coordinates of the reflected point are .
See Also
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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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