BTGmoderatorDC wrote:The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
A. 0
B. 2/5
C. 4/7
D. 1
E. 7/4
To partition the rectangle into equal areas, the line must pass through the CENTER of the rectangle.
To determine the x-coordinate of the center, take the average of the x-coordinates that form the base:
(0+7)/2 = 3.5.
To determine the y-coordinate of the center, take the average of the y-coordinates that form the left side:
(0+4)/2 = 2.
Thus, the center of the rectangle = (3.5, 2).
Since the line must pass through (2, 2) and (3.5, 2), we get the following slope:
(2 - 2)/(3.5 - 2) = 0.
The correct answer is
A.
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