Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -5 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions? Choose the correct option
A) 54
B) 1440
C) 2,160
D) 2,916
E) 148,824
We have the rectangle with dimensions 9*5 (9 horizontal dots and 5 vertical). AB is parallel to y-axis and AC is parallel to x-axis.   Choose the (x,y) coordinates for vertex A: 9C1*5C1;   Choose the x coordinate for vertex C (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 B (as x coordinate is fixed by A): 4C1, (5-1=4 as 1 vertical dot is already occupied by A).   9C1*5C*8C1*4C1=1440.   Answer: 1440.
<result>B</result>
Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -5 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?