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A right triangle ABC has to be constructed in the xyplane so that the
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22 May 2010, 14:05
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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: A right triangle ABC has to be constructed in the xyplane so that the
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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: A right triangle ABC has to be constructed in the xyplane so that the
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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: A right triangle ABC has to be constructed in the xyplane so that the
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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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Re: A right triangle ABC has to be constructed in the xyplane so that the
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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: A right triangle ABC has to be constructed in the xyplane so that the
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21 Dec 2010, 08:15



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Re: A right triangle ABC has to be constructed in the xyplane so that the
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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 so that the
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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 so that the
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10 Feb 2019, 22:36
Solution: Let’s draw a diagram to analyze the question: Attachment:
image1.PNG [ 17.14 KiB  Viewed 2800 times ]
Right angled triangle ABC, right angled at A, satisfying the following conditions: 3 ≤x1, x2≤ 5 and 2 ≤y1, y2≤ 11 Let the x and y coordinates for vertex A = (x1 and y1) Let the x and y coordinates for vertex B = (x1 and y2) [As AB is parallel to Y Axis, “x” coordinate will be same as the vertex A only “Y” coordinate will change.] Let the x and y coordinates for vertex C = (x2 and y1) [As AC is parallel to X Axis, “y” coordinate will be same as the vertex A only “X” coordinate will change.] So, as the diagram represents the number of triangles with the given conditions will vary as x1 and x2’s and y1 and y2’s vary. The total number of possibilities of triangles = x1 ×x2 ×y1 ×y2 = 9C1 8C1 10C1 9C1 = 6480 The correct answer option is “B”
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Re: A right triangle ABC has to be constructed in the xyplane so that the
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14 Mar 2019, 21:04
Bunuel wrote: 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. hi sir , i do understand all the algebra and combinations leading to the answer , but while selecting points don't we have to consider the validity of pythagoras theorem ? , such that the selected coordinates satisfy it as it is a right triangle , as our selection criteria seems to be based on just selecting points



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Re: A right triangle ABC has to be constructed in the xyplane so that the
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Re: A right triangle ABC has to be constructed in the xyplane so that the
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