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A right triangle ABC has to be constructed in the xy-plane [#permalink]

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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

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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press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

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.

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).

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?

Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

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11 Jan 2014, 03:43

Hello from the GMAT Club BumpBot!

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Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

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30 Jul 2014, 05:55

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[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

Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

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19 Sep 2015, 22:06

Hello from the GMAT Club BumpBot!

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Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

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29 Sep 2016, 14:15

Hello from the GMAT Club BumpBot!

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