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udaymathapati
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
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Units digit has to be 4 to quicken answer choice. 9*7*8*6 = 3024

Hope this helps
Cheers
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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
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Its not given that x,y has to be integer values only.
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zisis
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


1) Select the x coordinate of 2 vertices parallel to x-axis from -1 to 7: 9P2 = \frac{9!}{(9-2)!}= 9*8 ways
2) Select the y coordinate of A: 7 ways
3) Select the y coordinate of the 3rd point: 6 ways

Required answer = 9*8*7*6 = 3024

D is the correct answer
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tomcruiseh
Its not given that x,y has to be integer values only.

You're right tomcruiseh

bb
Bunuel
can you please check this? I think it's a typo.
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udaypratapsingh99
tomcruiseh
Its not given that x,y has to be integer values only.

You're right tomcruiseh

bb
Bunuel
can you please check this? I think it's a typo.

Fixed that. Thank you for reporting.
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