Math
posted by Theo on .
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 xaxis is 14, while the area that falls below the xaxis 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 rightangled 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