Difference between revisions of "1994 AJHSME Problems/Problem 4"

 
(One intermediate revision by one other user not shown)
Line 38: Line 38:
 
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 00:13, 5 July 2013

Problem

Which of the following represents the result when the figure shown below is rotated clockwise $120^\circ$ 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]

[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]

Solution

Rotating the circle $120^\circ$ is $1/3$ of a full turn. Going $1/3$ 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, $\boxed{\text{(B)}}$.

See Also

1994 AJHSME (ProblemsAnswer KeyResources)
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. AMC logo.png