1997 AHSME Problems/Problem 25
Problem
Let be a parallelogram and let
,
,
, and
be parallel rays in space on the same side of the plane determined by
. If
,
,
, and
and
and
are the midpoints of
and
, respectively, then
Solution
Let be a unit square with
,
,
, and
. Assume that the rays go in the +z direction. In this case,
,
,
, and
. Finding the midpoints of
and
gives
and
. The distance
is
, and the answer is
.
While this solution is not a proof, the problem asks for a value that is supposed to be an invariant. Additional assumptions that are consistient with the problem's premise should not change the answer. The assumptions made in this solution are that
is a square, and that all rays
are perpendicular to the plane of the square. These assumptions are consistient with all facts of the problem. Additionally, the assumptions allow for a quick solution to the problem.
See also
1997 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.