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27 Feb 2009, 05:15
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Right triange 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 constructed??
A 110
B 1100
C 9900
D 10000
E 12100
A 110
B 1100
C 9900
D 10000
E 12100
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27 Feb 2009, 08:14
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E
different variants for x: 4+5+1=10 (4 negative points, 5 positive and zero)
different variants for y: 16-6+1=11 (top coordinate - bottom coor. + 1..can't explain, count with fingers
)
PR parallel to ox, so we need different variants for x: for 2 points P and Q
PQ parallel to oy, ... P and R
so all possible triagles ... 10*10*11*11 = 12100
different variants for x: 4+5+1=10 (4 negative points, 5 positive and zero)
different variants for y: 16-6+1=11 (top coordinate - bottom coor. + 1..can't explain, count with fingers
)PR parallel to ox, so we need different variants for x: for 2 points P and Q
PQ parallel to oy, ... P and R
so all possible triagles ... 10*10*11*11 = 12100
