2020 AMC 12A Problems/Problem 17
Contents
Problem 17
The vertices of a quadrilateral lie on the graph of , and the
-coordinates of these vertices are consecutive positive integers. The area of the quadrilateral is
. What is the
-coordinate of the leftmost vertex?
Solution 1
Let the left-most -coordinate be
Recall that, by the shoelace formula, the area of the triangle must be That equals to
The -coordinate is, therefore,
~lopkiloinm.
Solution 2
Like above, use the shoelace formula to find that the area of the triangle is equal to . Because the final area we are looking for is
, the numerator factors into
and
, which one of
and
has to be a multiple of
and the other has to be a multiple of
. Clearly, the only choice for that is
~Solution by IronicNinja
See Also
2020 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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