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MATH / As shown below, convex pentagon ABCDE has sides AB=3, BC=4, CD=6, DE=3, and EA=7. The pentagon is originally positioned in the plane with vertex A at the origin and vertex B on the…

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problem

As shown below, convex pentagon ABCDEABCDE has sides AB=3AB=3, BC=4BC=4, CD=6CD=6, DE=3DE=3, and EA=7EA=7. The pentagon is originally positioned in the plane with vertex AA at the origin and vertex BB on the positive xx-axis. The pentagon is then rolled clockwise to the right along the xx-axis. Which side will touch the point x=2009x=2009 on the xx-axis? Enter "AB", "BC", "CD", "DE", or "EA". [asy] unitsize(3mm); defaultpen(linewidth(.8pt)); dotfactor=4; pair A=(0,0), Ep=7*dir(105), B=3*dir(0); pair D=Ep+B; pair C=intersectionpoints(Circle(D,6),Circle(B,4))[1]; pair[] ds={A,B,C,D,Ep}; dot(ds); draw(B--C--D--Ep--A); draw((6,6)..(8,4)..(8,3),EndArrow(6)); xaxis("xx",-8,14,EndArrow(3)); label("EE",Ep,NW); label("DD",D,NE); label("CC",C,E); label("BB",B,SE); label("(0,0)=A(0,0)=A",A,SW); label("33",midpoint(A--B),N); label("44",midpoint(B--C),NW); label("66",midpoint(C--D),NE); label("33",midpoint(D--Ep),S); label("77",midpoint(Ep--A),W); [/asy]
Plain-text mathematical notation (without MathML)
As shown below, convex pentagon ABCDE has sides AB=3, BC=4, CD=6, DE=3, and EA=7. The pentagon is originally positioned in the plane with vertex A at the origin and vertex B on the positive x-axis. The pentagon is then rolled clockwise to the right along the x-axis. Which side will touch the point x=2009 on the x-axis?

Enter "AB", "BC", "CD", "DE", or "EA".

[asy] unitsize(3mm); defaultpen(linewidth(.8pt)); dotfactor=4;  pair A=(0,0), Ep=7*dir(105), B=3*dir(0); pair D=Ep+B; pair C=intersectionpoints(Circle(D,6),Circle(B,4))[1]; pair[] ds={A,B,C,D,Ep};  dot(ds); draw(B--C--D--Ep--A); draw((6,6)..(8,4)..(8,3),EndArrow(6)); xaxis("x",-8,14,EndArrow(3));  label("E",Ep,NW); label("D",D,NE); label("C",C,E); label("B",B,SE); label("(0,0)=A",A,SW);  label("3",midpoint(A--B),N); label("4",midpoint(B--C),NW); label("6",midpoint(C--D),NE); label("3",midpoint(D--Ep),S); label("7",midpoint(Ep--A),W); [/asy]
Original LaTeX notation
As shown below, convex pentagon $ABCDE$ has sides $AB=3$, $BC=4$, $CD=6$, $DE=3$, and $EA=7$. The pentagon is originally positioned in the plane with vertex $A$ at the origin and vertex $B$ on the positive $x$-axis. The pentagon is then rolled clockwise to the right along the $x$-axis. Which side will touch the point $x=2009$ on the $x$-axis?

Enter "AB", "BC", "CD", "DE", or "EA".

[asy] unitsize(3mm); defaultpen(linewidth(.8pt)); dotfactor=4;  pair A=(0,0), Ep=7*dir(105), B=3*dir(0); pair D=Ep+B; pair C=intersectionpoints(Circle(D,6),Circle(B,4))[1]; pair[] ds={A,B,C,D,Ep};  dot(ds); draw(B--C--D--Ep--A); draw((6,6)..(8,4)..(8,3),EndArrow(6)); xaxis("$x$",-8,14,EndArrow(3));  label("$E$",Ep,NW); label("$D$",D,NE); label("$C$",C,E); label("$B$",B,SE); label("$(0,0)=A$",A,SW);  label("$3$",midpoint(A--B),N); label("$4$",midpoint(B--C),NW); label("$6$",midpoint(C--D),NE); label("$3$",midpoint(D--Ep),S); label("$7$",midpoint(Ep--A),W); [/asy]

level

Level 2

type

Intermediate Algebra

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Source and history

task_id
80c70a3c-30c9-5f5e-9455-7aa9e06ad1af
task_key
intermediate~5falgebra--test--80c70a3c-30c9-5f5e-9455-7aa9e06ad1af
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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