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A right triangle ABC has to be constructed in the xy-plane 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 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
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Re: A right triangle ABC has to be constructed in the xy-plane 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 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: A right triangle ABC has to be constructed in the xy-plane 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 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: A right triangle ABC has to be constructed in the xy-plane 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.
Consider giving me KUDOS if you find my post useful.
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Re: A right triangle ABC has to be constructed in the xy-plane so that the
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21 Dec 2010, 08:10
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: A right triangle ABC has to be constructed in the xy-plane 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 xy-plane 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 xy-plane so that the
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30 Jul 2014, 05:55
[quote="shekar123"]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
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 x-coordinate the point A can take any value from 2 to 11 (11-2+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 co-ordinate 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 xy-plane 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 xy-plane 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 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. 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 xy-plane so that the
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Re: A right triangle ABC has to be constructed in the xy-plane so that the
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