Each of the four examples on this page shows two colored regions in the plane. Your job is to find a straight-line cut which simultaneously divides each region exactly in half. In the left column, click and drag on the picture to draw a black line. The bars at the bottom show what fraction of each region is above the line. Your job is to drag the line around (drag either controlling point) until both regions are split exactly 50-50.

If you get stuck, try the applets in the right column. Here, you simply select (with the slider at the bottom) the direction of the cut. The computer calculates and draws for you the lines (in that direction) that would split each region in half. As you turn the direction, notice that those lines are sometimes far apart (meaning that no single line could do a good job of splitting both regions) and sometimes closer together. Your job now is merely to find a direction where the two lines coincide.

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