Difference between revisions of "1994 AJHSME Problems/Problem 4"
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| + | ==Problem== | ||
| + | |||
Which of the following represents the result when the figure shown below is rotated clockwise <math>120^\circ</math> about its center? | Which of the following represents the result when the figure shown below is rotated clockwise <math>120^\circ</math> about its center? | ||
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label("(E)",(48,5),N); | label("(E)",(48,5),N); | ||
</asy> | </asy> | ||
| + | |||
| + | ==Solution== | ||
| + | Rotating the circle <math>120^\circ</math> is <math>1/3</math> of a full turn. Going <math>1/3</math> clockwise of a full loop around the circle, the triangle would replace the square, the square would replace, the circle, and the circle would replace the triangle, <math>\boxed{\text{(B)}}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1994|num-b=3|num-a=5}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:13, 4 July 2013
Problem
Which of the following represents the result when the figure shown below is rotated clockwise 
about its center?
![[asy] unitsize(6); draw(circle((0,0),5)); draw((-1,2.5)--(1,2.5)--(0,2.5+sqrt(3))--cycle); draw(circle((-2.5,-1.5),1)); draw((1.5,-1)--(3,0)--(4,-1.5)--(2.5,-2.5)--cycle); [/asy]](http://latex.artofproblemsolving.com/3/4/5/345a68ccc30ab7fe4809574d1f1c1c365988d5a1.png)
![[asy] unitsize(6); for (int i = 0; i < 5; ++i) { draw(circle((12*i,0),5)); } draw((-1,2.5)--(1,2.5)--(0,2.5+sqrt(3))--cycle); draw(circle((-2.5,-1.5),1)); draw((1.5,-1)--(3,0)--(4,-1.5)--(2.5,-2.5)--cycle); draw((14,-2)--(16,-2)--(15,-2+sqrt(3))--cycle); draw(circle((12,3),1)); draw((10.5,-1)--(9,0)--(8,-1.5)--(9.5,-2.5)--cycle); draw((22,-2)--(20,-2)--(21,-2+sqrt(3))--cycle); draw(circle((27,-1),1)); draw((24,1.5)--(22.75,2.75)--(24,4)--(25.25,2.75)--cycle); draw((35,2.5)--(37,2.5)--(36,2.5+sqrt(3))--cycle); draw(circle((39,-1),1)); draw((34.5,-1)--(33,0)--(32,-1.5)--(33.5,-2.5)--cycle); draw((50,-2)--(52,-2)--(51,-2+sqrt(3))--cycle); draw(circle((45.5,-1.5),1)); draw((48,1.5)--(46.75,2.75)--(48,4)--(49.25,2.75)--cycle); label("(A)",(0,5),N); label("(B)",(12,5),N); label("(C)",(24,5),N); label("(D)",(36,5),N); label("(E)",(48,5),N); [/asy]](http://latex.artofproblemsolving.com/f/4/7/f47a55bc62a8d92426b4e7b5274663eedfe64954.png)
Solution
Rotating the circle is 
of a full turn. Going clockwise of a full loop around the circle, the triangle would replace the square, the square would replace, the circle, and the circle would replace the triangle, 
.
See Also
| 1994 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
