A right triangle AEC has to be constructed in the xy-plane so that the right angle is at A and AE is parallel to x axis. The coordinates of A, E 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?	Pick one:
A) 63	B) 336	C) 567	D) 3024	E) 5040

Rationale: all the cordinates are integer hence , possible ae values are { - 10 } , { - 11 } . . . . { - 17 } : 8 ways . . . . { 7 , - 1 } , { 70 } . . . . . . { 76 } : 8 ways 9 * 8 ways = 72 for ac values can be { 12 } , { 13 } . . . . { 17 } : 6 ways . . . . . . { 71 } , { 72 } . . . . . { 76 } : 6 ways 7 * 6 = 42 total = 72 * 42 = 3024 hence d
Answer: D