1992 AHSME Problems/Problem 24
Revision as of 07:24, 20 February 2018 by Hapaxoromenon (talk | contribs) (Added a little more detail to the solution)
Problem
Let be a parallelogram of area
with
and
. Locate
and
on segments
and
, respectively, with
. Let the line through
parallel to
intersect
at
. The area of quadrilateral
is
Solution
Use vectors. Place an origin at
, with
. We know that
, and also
, and now we can find the area of
by dividing it into two triangles and using cross-products (the expressions simplify using the fact that the cross-product distributes over addition, it is anticommutative, and a vector crossed with itself gives zero).
See also
1992 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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