2014 AMC 10A Problems/Problem 14
Problem
The -intercepts,
and
, of two perpendicular lines intersecting at the point
have a sum of zero. What is the area of
?
Solution
Note that if the
-intercepts have a sum of
, the distance from the origin to each of the intercepts must be the same. Call this distance
. Since the
, the length of the median to the midpoint of the hypotenuse is equal to half the length of the hypotenuse. Since the median's length is
, this means
, and the length of the hypotenuse is
. Since the
-coordinate of
is the same as the altitude to the hypotenuse,
.
See Also
2014 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AMC 10 Problems and Solutions |
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