agni_h1 wrote:A triangle ABC has to be constructed in xy plane so that the right angle is at A and AB is parallel to the x axis.The co-ordinates of A,B and C are to satisfy the inequlities -6<=x<=2 and 1<=y<=11.How many different triangles can be constructed with these properties ?

A.792
b.990
c.3024
d.7920
e.9900[/img]

IMO D

explanation goes like this.

Right angle triangle ABC has a right angle at A and AB is parallel to the X axis. That implies, x coordinate of A and C are same. Y coordinate of A and B are same.

For A possible values: X coordinate =9C1(-6 to 2) & 11C1(1 to 11)=99
For B possible values: X coordinate = 8C1(you have to leave out one value otherwise distance between A and B would be 0) Y coordinate=same as Y coordinate of A,which is already counted above.
For B possible values: X coordinate = same as X coordinate of A, which is already counted above. Y coordinate= 10C1=10

therefore, possible values=99*8*10=7920