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.
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