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GeoGebra

Weighted Average Exploration

Author:E.B. K, Steve Phelps, Tom Owsiak, Dang Do
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). Be certain to play around with this applet to get a feel for how the weighted average is calculated and how it behaves.

Task 1: Explore the diagram by moving the points and changing their weights. Answer the questions below.

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?

The weighted average is also known as the center of mass. Explore how the center of mass changes as the points and their masses change.

Task 2: The park director wants to install 2 drinking fountains. The water fountain, the playground, and the baseball field are to be equidistant apart. Where will the 2 drinking fountains be installed?

Task 3: Your job is to paint parking spaces and your boss asked you to paint a line segment perpendicular to the yellow line. The painted line must also go through point P.

Task 4: The school's emblem is a regular hexagon. You are to inscribed the emblem in the blue circle at the center of the basketball court.

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