A right triangle ABC has to be constructed in the xy-plane

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

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

Hope this helps
Cheers
J

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

Its not given that x,y has to be integer values only.

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

You're right tomcruiseh

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

Fixed that. Thank you for reporting.