Weighted Average Exploration

In this exploration, you can drag the points (A, B, C, D, E, and F) along the number line. You can type in weights for each point on the number line. For example, in the applet below, point A is at -4, and has a weight of 3. Therefore, the weighted point A contributes -12 to the overall average calculation (-4x3). How can you make the the weighted average equal to 0 without using zero weights? How can you make the the weighted average equal to 1? Can you do this in more than one way? Be certain to play around with this applet to get a feel for how the weighted average is calculated and how it behaves.