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Revision as of 19:55, 3 July 2013
Problem
Points 
and 
are the midpoints of sides 
and 
of 
. As 
moves along a line that is parallel to side 
, how many of the four quantities listed below change?
(a) the length of the segment 
(b) the perimeter of
(c) the area of
(d) the area of trapezoid 
![[asy] draw((2,0)--(8,0)--(6,4)--cycle); draw((4,2)--(7,2)); draw((1,4)--(9,4),Arrows); label("$A$",(2,0),SW); label("$B$",(8,0),SE); label("$M$",(4,2),W); label("$N$",(7,2),E); label("$P$",(6,4),N); [/asy]](http://latex.artofproblemsolving.com/0/b/6/0b66755a2c42a83a93ad849254ee5df3266bb45c.png)
Solution
(a) Clearly does not change, and 
, so doesn't change either.
(b) Obviously, the perimeter changes.
(c) The area clearly doesn't change, as both the base and its corresponding height remain the same.
(d) The bases and do not change, and neither does the height, so the trapezoid remains the same.
Only 
quantity changes, so the correct answer is 
.
See Also
| 2000 AMC 10 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 AMC 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
