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A right triangle ABC has to be constructed in the xyplane
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22 May 2010, 14:05
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74% (01:53) correct 26% (02:46) wrong based on 534 sessions
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A right triangle ABC has to be constructed in the xyplane 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
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Re: 700 + question
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23 May 2010, 05:06
shekar123 wrote: Please help me with this question
A right triangle ABC has to be constructed in the xyplane 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 xaxis and AC is parallel to yaxis. 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, (91=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, (101=9 as 1 vertical dot is already occupied by A). 9C1*10C1*8C1*9C1=6480. Answer: B.
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Re: 700 + question
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22 May 2010, 20:54
shekar123 wrote: Please help me with this question
A right triangle ABC has to be constructed in the xyplane 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 xcoordinate as A. Similarly C has 9 possibilities. Total: 90*8*10= 7200



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Re: 700 + question
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23 May 2010, 04:48
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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geometry  triangle
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21 Dec 2010, 08:10
A right triangle ABC has to be constructed in the xyplane 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
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21 Dec 2010, 08:15



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Re: 700 + question
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15 Jun 2011, 23:41
A 9*10 for x and y.
B 8* 1
C 1* 9



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Re: A right triangle ABC has to be constructed in the xyplane
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30 Jul 2014, 05:55
[quote="shekar123"]A right triangle ABC has to be constructed in the xyplane 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
Sol:
let's find point A first: X axis_ point A :: point A can be any where between 3 and 5 on X axis (total point = 5(3)+1 = 9)= 9c1 Y axis_ point A :: for each xcoordinate the point A can take any value from 2 to 11 (112+1) in Y coordinate= 10c1
A : 9c1*10c1
Lets Now find point B :
X axis _ Point B:: from remaining X cordinates( A has already taken one), B can take any value so 8C1 Y  axis_point B :: No bother because it will be on same coordinate as A
B: 8C1
Now point C: X: It has to be alias with A so no bother Y: It can take any value from remaining 9 (one already taken by A) , 9C1
total: 9c1*10c1*8c1*9c1 = 6480 !!!!



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Re: A right triangle ABC has to be constructed in the xyplane
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08 Jun 2018, 19:47
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Re: A right triangle ABC has to be constructed in the xyplane &nbs
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