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Triangle ABC will be constructed in a xy-plane according to

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Triangle ABC will be constructed in a xy-plane according to [#permalink] New post 14 May 2012, 14:32
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Triangle ABC will be constructed in a xy-plane according to the following conditions: Angle ABC is 90 degrees, and AB is parallel to the y-axis; for each of points A, B and C, both the x-coordinate and the y-coordinate must be integers; the range of possible x-coordinates is 0=<x=<5 and the range of possible y-coordinates is -4=<y=<6. Any two triangles with non-identical vertices are considered different. Given these constraints, how many different triangles could be constructed?

A. 50
B. 66
C. 2500
D. 3300
E. 4356
[Reveal] Spoiler: OA
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Re: Triangle ABC will be constructed in a xy-plane according to [#permalink] New post 14 May 2012, 22:47
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alexpavlos wrote:
Triangle ABC will be constructed in a xy-plane according to the following conditions: Angle ABC is 90 degrees, and AB is parallel to the y-axis; for each of points A, B and C, both the x-coordinate and the y-coordinate must be integers; the range of possible x-coordinates is 0=<x=<5 and the range of possible y-coordinates is -4=<y=<6. Any two triangles with non-identical vertices are considered different. Given these constraints, how many different triangles could be constructed?

A. 50
B. 66
C. 2500
D. 3300
E. 4356


Since give that 0=<x=<5 and -4=<y=<6 then we have a rectangle with dimensions 6*11 (6 horizontal and 11 vertical dots). AB is parallel to y-axis, BC is parallel to x-axis and the right angle is at B.

Choose the (x,y) coordinates for vertex B: 6C1*11C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by B): 5C1, (6-1=5 as 1 horizontal dot is already occupied by B);
Choose the y coordinate for vertex A (as x coordinate is fixed by B): 10C1, (11-1=10 as 1 vertical dot is already occupied by B).

6C1*11C1*5C1*10C1=3,300.

Answer: D.

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Hope it helps.
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Re: Triangle ABC will be constructed in a xy-plane according to   [#permalink] 14 May 2012, 22:47
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