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Right triangle PQR is to be constructed in the xy-plane so

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Right triangle PQR is to be constructed in the xy-plane so [#permalink] New post 26 Feb 2008, 18:51
248. Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y- coordinates of P, Q and R are to be integers that satisfy the inequalities -4≤x≤5 and 6≤y≤16. how many different triangles with these properties could be contructed?

A. 110
B. 1100
C. 9900
D. 10000
E. 12100
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Re: 248. triangle [#permalink] New post 27 Feb 2008, 05:47
# of ways to have a base:

10*9*11

10 ways to choose first x coordinate
9 ways to choose second x coordinate along same parallel line
11 ways to choose which level of y this is occuring at

# of ways to have 3rd vertex:

10

because we already have a base parallel to the x-axis, now we need one more line for the vertex. It has to have the same x coordinate (since it's a right angle) so there are 10 other y values it could have

10*9*11*10 = 9,900 different triangles

Answer C
Re: 248. triangle   [#permalink] 27 Feb 2008, 05:47
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Right triangle PQR is to be constructed in the xy-plane so

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