Difference between revisions of "2004 AMC 12B Problems/Problem 9"
(New page: == Problem == The point <math>(-3,2)</math> is rotated <math>90^\circ</math> clockwise around the origin to point <math>B</math>. Point <math>B</math> is then reflected over the line <mat...) |
(→See Also) |
||
| Line 37: | Line 37: | ||
{{AMC12 box|year=2004|ab=B|num-b=8|num-a=10}} | {{AMC12 box|year=2004|ab=B|num-b=8|num-a=10}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 18:56, 3 July 2013
Problem
The point 
is rotated 
clockwise around the origin to point 
. Point is then reflected over the line 
to point 
. What are the coordinates of ?
Solution
The entire situation is in the picture below. The correct answer is 
.
![[asy] unitsize(1cm); defaultpen(0.8); pair A=(-3,2), B=rotate(-90)*A, C=(3,2); dot(A); dot(B); dot(C); draw( A -- (0,0) -- B -- C, Dotted ); draw( (-3,-3) -- (4,4), dashed ); label("$A=(-3,2)$", A, NW ); label("$B=(2,3)$", B, N ); label("$C=(3,2)$", C, E ); label("$x=y$",(4,4),NE); dot((0,0)); label("$(0,0)$", (0,0), SE); [/asy]](http://latex.artofproblemsolving.com/5/c/8/5c86b2e7e7f1e8eda5185b38ddd190d011cf750a.png)
See Also
| 2004 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
