BTGmoderatorDC wrote:ABCD is a rectangle which is constructed in the xy-plane. The length AB lies on the x-axis and AD on the y-axis. If the x-coordinate of vertices B and C and y coordinates of vertices C and D are integers that satisfy the inequality 7<=x<=18. and -7<=y<=12 respectively, how many rectangles can be constructed, which satisfy the above properties?
A. 100
B. 120
C. 228
D. 240
E. 360
Since AB lies on the x-axis and AD lies on the y-axis, the coordinates for ABCD are determined solely by the coordinates for C.
For example, if C = (7, 12), the following rectangle is yielded:
D (0,12)...................................(7,12) C
A (0,0).......................................(7,0) B
Implication:
The number of possible rectangles is equal to the NUMBER OF OPTIONS FOR C.
Number of ways to choose an x-coordinate for C = 12. (Any integer between 7 and 18, inclusive.)
Number of ways to choose a y-coordinate for C = 19. (Any integer between -7 and 12, inclusive, except for 0, since C cannot lie on the x-axis.)
To combine our options for the x-coordinate with our options for the y-coordinate, we multiply:
12*19 = 228
The correct answer is
C.
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