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A right triangle ABC has to be constructed in the xy-plane
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08 Sep 2010, 12:21
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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 coordiantes of A, B and C are to satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. The numbers of different triangles that can be constructed with these properties are?
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 coordiantes of A, B and C are to satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. The numbers of different triangles that can be constructed with these properties are?
A63 B336 C567 D3024 E5040
Question should specify that x- and y-coordinates of A, B, and C are to be integers.
We have the rectangle with dimensions 9*7 (9 horizontal dots and 7 vertical). AC is parallel to y-axis and AB is parallel to x-axis.
Choose the (x,y) coordinates for vertex A (right angle): 9C1*7C1; 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): 6C1, (7-1=6 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 coordiantes of A, B and C are to satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. The numbers of different triangles that can be constructed with these properties are?
A63 B336 C567 D3024 E5040
Note: A and C share the same x coordinate. A and B share the same y coordinate.
The x coordinates have 9 options (x = -1,0,1,2,3,4,5,6,7) pick 2: 1 for point B, and 1 for point A and C. 9P2 The y coordinates have 7 options (y= 1,2,3,4,5,6,7) pick 2: 1 for point A and B, and 1 for point C. 7P2 Number of triangles w/ A as the right angle = 9P2 * 7P2 = 3024
A right triangle ABC has to be constructed in the xy-plane so that the
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22 Jun 2011, 03:11
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 integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
Re: A right triangle ABC has to be constructed in the xy-plane so that the
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Updated on: 22 Jun 2011, 03:22
udaymathapati wrote:
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 integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? A 63 B 336 C 567 D 3024 E 5040
Its D , for point A you can use any of 9 points ( Xaxis) and & 7 points ( y axis points).. hence 63 ways for B he can use any other 8 points on the X axis and for C .. any of the other 6 points. so total 63*8*6 = 3024
Originally posted by sudhir18n on 22 Jun 2011, 03:21.
Last edited by sudhir18n on 22 Jun 2011, 03:22, edited 1 time in total.
Re: A right triangle ABC has to be constructed in the xy-plane so that the
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08 Jul 2011, 08:05
udaymathapati wrote:
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 integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? A 63 B 336 C 567 D 3024 E 5040
All the cordinates are integer hence, possible AB values are {-1,0}, {-1,1} ....{-1,7}: 8 ways .... {7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be {1,2}, {1,3} .... {1,7} : 6ways ...... {7,1}, {7,2} ..... {7,6} : 6 ways
Re: A right triangle ABC has to be constructed in the xy-plane
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23 Feb 2015, 07:56
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Quote:
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 coordiantes of A, B and C are to satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. The numbers of different triangles that can be constructed with these properties are?
A. 63 B. 336 C. 567 D. 3024 E. 5040
Here we have a rectangle of size 9*7. There are 9 choices for the x coordinate {-1,0,1,2,3,4,5,6,7} There are 7 choices for the y coordinate {1,2,3,4,5,6,7} AB is parallel to the x-axis, so both A & B will have the same y-coordinate. Let us say that is p AC is parallel to the y-axis, so both A & C will have the same x-coordinate. Let us say that is q Let us assume the y coordinate of x coordinate of B to be r and the y-coordinate of C be s So, the coordinates of A are (q,p); B are (r,p); and C are (q,s)
We need to find out overall possible values for p,q,r,s
q and r need to be chosen from the 9 choices for x-coordinate => q & r can be chosen in 9*8 = 72 ways
p and s need to be chosen from the 8 choices for y-coordinate => p & s can be chosen in 7*6 = 42 ways Total ways = 72*42 = 3024 Correct Answer: D
Re: A right triangle ABC has to be constructed in the xy-plane
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22 May 2018, 05:07
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