Interact with the applet below for a few minutes. [br][br]Be sure to change the locations of the [b][color=#cc0000]red point[/color][/b] and [b][color=#9900ff]purple point[/color][/b] each time before re-sliding the slider. [br][br](For this illustration, assume lines that appear to be parallel [i]are[/i] parallel.) [br][br]After doing so, please answer the questions that follow.
What can we conclude about the area of the [b][color=#38761d]green rectangle[/color][/b] and the area of the [b][color=#bf9000]yellow rectangle[/color][/b]? Why can we conclude this?
Why does the area of the [b][color=#38761d]green rectangle[/color][/b] never change (despite the transformations we see)?
[b][color=#9900ff]Suppose the length of the purple segment = 2. [/color][/b][br][b][color=#cc0000]Suppose the length of the red segment = 3. [/color][/b][br][br]What would the length of the [b]single-tick segment[/b] be (in terms of [i]a[/i])? [br]What would the length of the [b]double-tick segment[/b] be (in terms of [i]a[/i])?
Given the information in (3), what would the length of the vertical segment (farthest to the right) be? (Express in terms of [i]a[/i]).
Given your response for (1), write a relationship (equation) that contains the expressions you wrote for (3) and (4) above.
In general, what property (law) of exponents does this animation help illustrate? Explain.