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2000 AMC 10 #5

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August 27, 2011
geometryperimetertrapezoid

Problem Statement

Points MM and NN are the midpoints of sides PAPA and PBPB of △PAB\triangle PAB. As PP moves along a line that is parallel to side ABAB, how many of the four quantities listed below change?
(A) the length of the segmentMN\mathrm{(A)}\ \text{the length of the segment} MN
(B) the perimeter of △PAB\mathrm{(B)}\ \text{the perimeter of }\triangle PAB
(C)  the area of △PAB\mathrm{(C)}\ \text{ the area of }\triangle PAB
(D)  the area of trapezoidABNM\mathrm{(D)}\ \text{ the area of trapezoid} ABNM
[asy] draw((2,0)--(8,0)--(6,4)--cycle); draw((4,2)--(7,2)); draw((1,4)--(9,4),Arrows); label("AA",(2,0),SW); label("BB",(8,0),SE); label("MM",(4,2),W); label("NN",(7,2),E); label("PP",(6,4),N);[/asy]
(A) 0(B) 1(C) 2(D) 3(E) 4\mathrm{(A)}\ 0 \qquad\mathrm{(B)}\ 1 \qquad\mathrm{(C)}\ 2 \qquad\mathrm{(D)}\ 3 \qquad\mathrm{(E)}\ 4
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