Math
posted by Kiki 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), 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.

Draw the figure. The area is 32.
The area above the xaxis 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.