2020 AMC 12A Problems/Problem 17
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.