rahulvsd wrote:Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 3 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Number of possible x-coordinates = (11 - 3) + 1 = 9
Number of possible y-coordinates = (5 - (-5)) + 1 = 11
Any rectangle drawn in the coordinate plane with sides parallel to the x- and y-axes will have vertices with coordinates of the form (a, b), (c, b), (c, d) and (a, d).
Hence, we can conclude that two x-coordinates (a and c here) and two y-coordinates (b and d here) are enough to define such a rectangle.
Hence, number of such rectangles = (Number of ways to select two x-coordinates from 9)*(Number of ways to select two y-coordinates from 11) = (9
C2)*(11
C2) = (9*8/2)*(11*10/2) = (11*10*9*2) = (22*90) = 1980
The correct answer is C.
