Math

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) nad (0,-7), in this order. Determine the slope of a line that passes through the origin and divides the letter F into two regions of equal area.

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asked by Theo
  1. Cute question.

    After you made your sketch, you will find that the area above the x-axis is 14, while the area that falls below the x-axis is 18, so we have to cut off 2 units from the rectangle formed by (0,0), (4,0), (4,-2) and (0,-2).
    That will result in a right-angled triangle with base 4 and height h such that
    (1/2)(4)h = 2
    h = 1

    so the line has to go through the point (4,-1)
    resulting in a slope of -1/4

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    posted by Reiny

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