bml1105 wrote:The vertices of a rectangle in the standard (x,y) coordinate plane 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
OA: A
A rectangle can be divided into 2 regions with equal areas in 3 ways : either by a diagonal that divides rectangle into 2 triangles with equal areas or
by a vertical line that passes through the mid point of its length that divides rectangle into 2 smaller rectangles or
by a horizontal line that passes through the mid point of the width of the rectangle.
If you draw the rectangle using the given vertices on a coordinate plane, you will find that (2,2) lies on the horizontal line that passes through the mid point of the width of rectangle. This line divides the rectangle into 2 smaller rectangles with length 7 units and width 2 units and same area. Slope of any line parallel to x axis (i.e a horizontal line) is always 0. This can be stated in other ways also, such as the angle made by this line with respect to x axis (in anti clockwise direction) is 0, slope of any line is the tangent of this angle and Tan 0 = 0.
So the correct answer is
A
Regards
Sukriti
