There's no such brush. Something resembling can be done filling a selection with color. You can make the selection as follows:
1) Draw the sweeping path in its start position, duplicate it
NOTE: make every path visible as soon as you have drawn it
2) Edit the duplicate to present the final sweep position
3) Draw new paths which present the routes of the endpoints
4) Merge visible paths
5) Edit the result to properly closed path. You have to connect point pairs by left clicking on them twice holding Ctrl key at the same time. After connecting points you can move them to exactly the same place. Before inserting the line segments also the node handles to outwards must be shortened to zero. Otherwise the result is unpredictable.
6) Convert path to selection
7) Fill the selection. You can paint, use the paint bucket or fill path. The color is inserted to the layer which is active in the layers panel.
Explore carefully the content of the Paths panel and the functions available with right click.
ADD: You seem to want shapes which have well defined edges - paths. In vector graphics programs they are the main subject. Get Inkscape if you haven't one. It's free.