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A right triangle ABC has to be constructed in the xy-plane

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A right triangle ABC has to be constructed in the xy-plane [#permalink] New post 22 May 2010, 15:05
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A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

A. 100
B. 6480
C. 2320
D. 1500
E. 9000


my analysis

A(x,y) - 9,10- 90 possible values
B(x,y) - 8,10 =80 possible values
C(X,Y) -9,9 =81 POBBILE VALUES

i DON'T KNOW HOW TO PROCEED LATER
[Reveal] Spoiler: OA
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Re: 700 + question [#permalink] New post 22 May 2010, 21:54
shekar123 wrote:
Please help me with this question

A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

my analysis

A(x,y) - 9,10- 90 possible values
B(x,y) - 8,10 =80 possible values
C(X,Y) -9,9 =81 POBBILE VALUES

i DON'T KNOW HOW TO PROCEED LATER


You are going in the right direction. For A there are 90 possibilities. However, for B we are bound by A, so we have only 8 possibilities because B has to have the same x-coordinate as A. Similarly C has 9 possibilities.
Total: 90*8*10= 7200
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Re: 700 + question [#permalink] New post 23 May 2010, 05:48
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Friends,
Please provide the OA.
I am trying to provide my thinking below:
For A, there are 90 possibilities on the plane.
For each location of A, as the triangle has to have same properties, there are 8 possibilities on the x axis and 9 possibilities on y axis.
So the answer is 90*8*9 = 6480
Please provide the OA.

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Re: 700 + question [#permalink] New post 23 May 2010, 06:06
shekar123 wrote:
Please help me with this question

A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

my analysis

A(x,y) - 9,10- 90 possible values
B(x,y) - 8,10 =80 possible values
C(X,Y) -9,9 =81 POBBILE VALUES

i DON'T KNOW HOW TO PROCEED LATER


amitjash's solution is correct.

We have the rectangle with dimensions 9*10 (9 horizontal dots and 10 vertical). AB is parallel to x-axis and AC is parallel to y-axis.

Choose the (x,y) coordinates for vertex A: 9C1*10C1=90;
Choose the x coordinate for vertex B (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex C (as x coordinate is fixed by A): 9C1, (10-1=9 as 1 vertical dot is already occupied by A).

9C1*10C1*8C1*9C1=6480.

Answer: B.
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Re: 700 + question [#permalink] New post 04 Nov 2010, 16:29
My answer is 9x10+8x1+1x9=6480
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geometry - triangle [#permalink] New post 21 Dec 2010, 09:10
A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

100
6480
2320
1500
9000
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Re: geometry - triangle [#permalink] New post 21 Dec 2010, 09:15
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Merging similar topics.

Also check: arithmetic-og-question-88380.html?hilit=constructed#p790651 and geometry-and-combinations-100675.html?hilit=constructed#p777591
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

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Re: 700 + question [#permalink] New post 16 Jun 2011, 00:41
A 9*10 for x and y.

B 8* 1

C 1* 9
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Re: 700 + question   [#permalink] 16 Jun 2011, 00:41
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