AMC 8 2004 Problem 23
Source:
July 23, 2011
analytic geometrygraphing linesslope
Problem Statement
Tess runs counterclockwise around rectangular block JKLM. She lives at corner J. Which graph could represent her straight-line distance from home?[asy]pair J=(0,6), K=origin, L=(10,0), M=(10,6);
draw(J--K--L--M--cycle);
label("", J, dir((5,3)--J));
label("", K, dir((5,3)--K));
label("", L, dir((5,3)--L));
label("", M, dir((5,3)--M));[/asy]
[asy]size(80);defaultpen(linewidth(0.8));
draw((16,0)--origin--(0,16));
draw(origin--(15,15));
label("time", (8,0), S);
label(rotate(90)*"distance", (0,8), W);
[/asy]
[asy]size(80);defaultpen(linewidth(0.8));
draw((16,0)--origin--(0,16));
draw((0,6)--(1,6)--(1,12)--(2,12)--(2,11)--(3,11)--(3,1)--(12,1)--(12,0));
label("time", (8,0), S);
label(rotate(90)*"distance", (0,8), W);
[/asy]
[asy]size(80);defaultpen(linewidth(0.8));
draw((16,0)--origin--(0,16));
draw(origin--(2.7,8)--(3,9)^^(11,9)--(14,0));
draw(Arc((4,9), 1, 0, 180));
draw(Arc((10,9), 1, 0, 180));
draw(Arc((7,9), 2, 180,360));
label("time", (8,0), S);
label(rotate(90)*"distance", (0,8), W);
[/asy]
[asy]size(80);defaultpen(linewidth(0.8));
draw((16,0)--origin--(0,16));
draw(origin--(2,6)--(7,14)--(10,12)--(14,0));
label("time", (8,0), S);
label(rotate(90)*"distance", (0,8), W);
[/asy]
[asy]size(80);defaultpen(linewidth(0.8));
draw((16,0)--origin--(0,16));
draw(origin--(3,6)--(7,6)--(10,12)--(14,12));
label("time", (8,0), S);
label(rotate(90)*"distance", (0,8), W);
[/asy]