# 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.