Exponent Law: Geometric Illustration
Interact with the applet below for a few minutes.
Be sure to change the locations of the red point and purple point each time before re-sliding the slider.
(For this illustration, assume lines that appear to be parallel are parallel.)
After doing so, please answer the questions that follow.
1.
What can we conclude about the area of the green rectangle and the area of the yellow rectangle? Why can we conclude this?
2.
Why does the area of the green rectangle never change (despite the transformations we see)?
3.
Suppose the length of the purple segment = 2.
Suppose the length of the red segment = 3.
What would the length of the single-tick segment be (in terms of a)?
What would the length of the double-tick segment be (in terms of a)?
4.
Given the information in (3), what would the length of the vertical segment (farthest to the right) be? (Express in terms of a).
5.
Given your response for (1), write a relationship (equation) that contains the expressions you wrote for (3) and (4) above.
6.
In general, what property (law) of exponents does this animation help illustrate? Explain.