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Difference between revisions of "2004 AMC 8 Problems/Problem 23"

(Created page with "==Problem== Tess runs counterclockwise around rectangular block <math>JKLM</math>. She lives at corner <math>J</math>. Which graph could represent her straight-line distance from...")
 
(Problem)
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==Problem==
 
==Problem==
 
Tess runs counterclockwise around rectangular block <math>JKLM</math>. She lives at corner <math>J</math>. Which graph could represent her straight-line distance from home?
 
Tess runs counterclockwise around rectangular block <math>JKLM</math>. She lives at corner <math>J</math>. Which graph could represent her straight-line distance from home?
 +
 +
<asy>
 +
unitsize(5mm);
 +
pair J=(-3,2); pair K=(-3,-2); pair L=(3,-2); pair M=(3,2);
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draw(J--K--L--M--cycle);
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label("$J$",J,NW);
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label("$K$",K,SW);
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label("$L$",L,SE);
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label("$M$",M,NE);
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</asy>
  
 
[[Image:AMC8200423.gif]]
 
[[Image:AMC8200423.gif]]

Revision as of 15:48, 24 December 2012

Problem

Tess runs counterclockwise around rectangular block $JKLM$. She lives at corner $J$. Which graph could represent her straight-line distance from home?

[asy] unitsize(5mm); pair J=(-3,2); pair K=(-3,-2); pair L=(3,-2); pair M=(3,2);  draw(J--K--L--M--cycle); label("$J$",J,NW); label("$K$",K,SW); label("$L$",L,SE); label("$M$",M,NE); [/asy]

AMC8200423.gif

Solution

For her distance to be represented as a constant horizontal line, Tess would have to be running in a circular shape with her home as the center. Since she is running around a rectangle, this is not possible, rulling out $B$ and $E$ with straight lines. Because $JL$ is the diagonal of the rectangle, and $L$ is at the middle distance around the perimeter, her maximum distance should be in the middle of her journey. The maximum in $A$ is at the end, and $C$ has two maximums, ruling both out. Thus the answer is $\boxed{\textbf{(D)}}$.

See Also

2004 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 22
Followed by
Problem 24
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
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