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# In the rectangular coordinate plane, a rectangular region has vertices

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Math Expert
Joined: 02 Sep 2009
Posts: 60578
In the rectangular coordinate plane, a rectangular region has vertices  [#permalink]

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12 Nov 2019, 03:56
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:36) correct 36% (03:10) wrong based on 39 sessions

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In the rectangular coordinate plane, a rectangular region has vertices (2.5, 4.5), (2.5, −1.5), (−7.5, -1.5), and (−7.5, 4.5). If a point from within the rectangle is to be randomly selected such that both the x- and y-coordinates are integers, what is the probability that both coordinates of the selected point are negative?

A. 1/11
B. 7/60
C. 2/15
D. 16/77
E. 4/15

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In the rectangular coordinate plane, a rectangular region has vertices  [#permalink]

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12 Nov 2019, 09:52
5
1
1
Given that the randomly chosen point should have X- & Y- coordinates as negative, the point should lie in the III Quadrant. => The point has to lie between X - (0 to -7.5) & Y - (0 to -1.5).
Also given that the coordinates for the randomly selected points are 'Negative integers'.
=>X can be any one of (-7,-6,-5,-4,-3,-2,-1) => 7C1
=> Y can be any one of (-1) => 1C1
=> Total combinations = 7C1*1C1 = 7

Total combinations for a point to lie anywhere in the rectangle =
X- (-7,-6,-5,-4,-3,-2,-1,0,1,2) & Y- (-1,0,1,2,3,4)
=> 10C1*6C1 = 10*6 = 60

=> Probability = 7/60

IMO B
In the rectangular coordinate plane, a rectangular region has vertices   [#permalink] 12 Nov 2019, 09:52
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