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Parallelogram $ABCD$ has vertices $A(3,3)$, $B(-3,-3)$, $C(-9,-3)$, and $D(-3,3)$. If a point is selected at random from the region determined by the parallelogram, what is the probability that the point is not above the $x$-axis? Express your answer as a common fraction.

 Jul 9, 2018
 #1
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Must the point have integer coordinates?

If so, list all the possible points, count how many are not above the x-axis and count the total number of points, and divide the answers.

If not, there are an infinite number of points possible. The number of points on the x-axis can be can be added to those below the x-axis without increasing the (infinite) number. Then, there will be as many points below the x-axis as above the x-axis, so the answer will be 1/2. 

 Jul 9, 2018

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