Geometry: Transformations
Transformational Geometry Applets, Discovery Learning Applets, etc...
Table of Contents
- Introduction
- Messing With Lisa
- Transformations: Exercise 1
- Dilations
- Dilating a Point (Intro)
- Dilating a Line: HSG.SRT.A.1.A
- Dilating a Segment: HSG.SRT.A.1.B
- Properties of Dilations
- AA Similarity Theorem
- Translations
- Rotations
- Rotations: Introduction
- Reflection About a Line
- Reflection About a Point
Messing With Lisa
Note: LARGE POINTS are MOVEABLE.
Dilating a Point (Intro)
[color=#000000]The following applet illustrates what it means to dilate a point about another point. [br][br]You can move [b]point [i]O [/i](the center of dilation)[/b] and [/color][color=#ff0000][b]point [i]A[/i][/b][/color][color=#000000] anywhere in the plane. [br]You can also change the [b]scale factor ([i]k[/i])[/b] of this dilation by either moving the slider or[br]by typing it in the white box at the top of the applet.[br][/color][b][color=#980000][i]A' = [/i]the image of point [i]A[/i] under dilation about point [i]O[/i] with scale factor [i]k[/i]. [br][/color][/b][br][color=#000000][b]Interact with the applet below for a few minutes [i]BEFORE[/i] clicking the "Check This Out!" checkbox in the lower right corner. [/b] [i]After interacting with this applet for a bit, please answer the questions that follow the applet. (You'll be prompted to click the "Check This Out!" checkbox in the directions below.) [/i][/color]
[color=#000000][b]Questions: (Please don't click the "Check This Out!" box yet!) [/b][/color][br][br][color=#000000]1) What vocab term would you use to describe the locations of point [i]A[/i] and [i]A'[/i] with [br] respect to [i]O[/i]? In essence, fill in the blank: "The [/color][color=#980000][b]image[/b][/color][color=#000000] of a [/color][color=#ff0000]point ([i]A[/i])[/color][color=#000000] under a dilation [/color][br][color=#000000] about another point ([/color][i]O[/i][color=#000000]) is a [/color][color=#980000][b]point ([i]A'[/i])[/b][/color][color=#000000] that is _____________________ with [/color][i]O[/i][color=#000000] and [/color][i]A[/i][color=#000000]. [/color][br][br][color=#000000]2) Click the "Check This Out!" box now. Move point(s) [/color][i]O[/i][color=#000000] and [/color][i]A[/i][color=#000000] around. Be sure to [br] adjust the scale factor ([/color][i]k[/i][color=#000000]) of this dilation as well. Describe what you observe.[br][br]3) Answer the additional questions on the sheet provided to you in class. [br][br] [/color]
Rotations: Introduction
[color=#000000]The applet below was designed to help you better understand what it means to rotate a point about another point. [br][br]In the applet below, feel free to change the locations of point [i]A[/i] and[/color] [color=#1e84cc]point [i]B[/i][/color]. [br][color=#000000]Interact with this applet for a few minutes, then answer the questions that follow.[/color]
[color=#000000][b]Questions: [/b][br][br]1) Regardless of the [/color][color=#1e84cc][b]amount of rotation[/b][/color][color=#000000], how does the distance [i]AC [/i]compare to the distance [i]AB[/i]? [br][br]2) Notice how, in the applet above, the [/color][color=#1e84cc][b]angle of rotation[/b][/color][color=#000000] could be [/color][color=#1e84cc][b]positive[/b][/color][color=#000000] or [/color][color=#1e84cc][b]negative[/b][/color][color=#000000].[br] From what you've observed, what does it mean for a [/color][color=#1e84cc][b]rotation angle[/b][/color][color=#000000] to have positive orientation? [br] What does it mean for an [/color][color=#1e84cc][b]angle of rotation[/b][/color][color=#000000] to have negative orientation? [br] Explain. [/color]