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The capital letter F can be formed by connecting the points (0,4),(5,4),(5,2),(2,2),(2,0),(4,0),(4,-2),(2,-2),(2,-7), and (0,-7), in this order. Determine the slope of the line that passes through the origin and divides the letter F into two regions of equal areas.

  • Math -

    Draw the figure. The area is 32.
    The area above the x-axis is 14, and below is 18.

    So, we want a line sloping down through the origin.

    Further inspection shows that the area of the foot is 10, so we want a chunk of area 6 in the middle section.

    That will be formed by a trapezoid of height 4 with bases 2 and b, such that

    (2+b)/2 * 4 = 6
    2+b = 3
    b = 1

    So, we want the line through (0,0) and (4,-1). That will have slope -1/4.

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