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OG PS 248

by Maggie12 » Tue Jan 27, 2009 2:24 pm
Hi


Need help on this....

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 < or= x < or = 5 and 6 < or= y < or = 16. How many different triangles with these properties could be constructed?
(A) 110
(B) 1,100
(C) 9,900
(D) 10,000
(E) 12,100
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by bstalling » Tue Jan 27, 2009 3:02 pm
Options for first point: (5--4+1)*(16-6+1) = 10*11 = 110 total options for first point based on the inequalities

Second point can be anywhere parallel x-axis, thus (10-1)*110 = 990

Third point is anywhere parallel to y-axis, thus (11-1)*990 = 9900 (C)
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