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> | ||
| + | |||
| + | == Solution == | ||
| + | |||
| + | The line <math>y = 2000</math> is a horizontal line located <math>12</math> units beneath the point <math>(1000, 2012)</math>. When a point is reflected about a horizontal line, only the <math>y</math> - coordinate will change. The <math>x</math> - coordinate remains the same. Since the <math>y</math>-coordinate of the point is <math>12</math> units above the line of reflection, the new <math>y</math> - coordinate will be <math>2000 - 12 = 1988</math>. Thus, the coordinates of the reflected point are <math>(1000, 1988)</math>. <math>\boxed{\textbf{(B)}}</math> | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AMC10 box|year=2012|ab=B|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 19:43, 15 February 2024
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
