Geometric Transformations (How-to)
This geogebra book will walk student through how to use the transformation tools in geogebra.
Inhaltsverzeichnis
- Creating a Polygon
- Creating a Polygon
- Translating a Polygon
- Translating A Polygon
- Reflecting a Polygon
- Reflecting a Polygon
- Rotating a Polygon
- Rotating a Polygon
- Dilating a Polyogn
- Dilating a Polygon
- Composition Of Transformations
- Problem #1
- Problem #2
- Congruence Transformations
- Essential Understanding: Congruence Transformation
- Congruence Transformations#1
- Congruence Transformation #2
Creating a Polygon
Create a polygon on top of the current polygon.
Step 1: Click[icon]/images/ggb/toolbar/mode_polygon.png[/icon] (4th button) [br]Step 2: Choose Polygon[br]Step 3: Create points A, B, C, and D below. After point D, connect points A and D to close the figure. [br]Step 4: Once your polygon is created. You can move it using any of the points. [br][br][b]Problem#1: Create a polygon with vertices A(-2, 1), B(1, 4), C(5, 4), and D(4, 1). [/b][br]**Take a screen shot of your work. Insert it into the appropriate google slide. [br]***Geogebra will NOT save your work!!!!
Translating A Polygon
Read the directions and complete the problems.
[br]Step 1: Create a polygon with vertices as described below. [br] A(1, 2) , B(3, 5), and C(6, 3) [br] [br]Step 2: Click [icon]/images/ggb/toolbar/mode_mirroratline.png[/icon] (button 8) [br]Step 3: Choose Translate by Vector [icon]/images/ggb/toolbar/mode_vectorfrompoint.png[/icon]. [br][br]Step 4: Translate the polygon[br] a) Click the polygon itself[br] b) Click point A. A "ray" will appear. This ray is a vector. [br] c) Click on a second point that moves the same left/right direction and up/down direction as the rule. Move the ray so that a second point is created. [br] For example: if your rule is T<-4, 3>([math]\bigtriangleup[/math]ABC), you will move the second point left 4 and up 3 from point A. [br][br]Step 5: When you've completed step 4, a translated triangle will automatically generate. [br][br]Step 6: Move point A' around. You will notice that the image moves according to the vector. [br][br][b]Problem #1: T<-4, 3>([/b][math]\bigtriangleup[/math][b]ABC)[br][br]Problem #2: T<5, 7>([/b][math]\bigtriangleup[/math][b]ABC)[br][br]*Perform each transformation within this applet. [br][br][/b]**Take a screen shot of your work (you will have problem #1 and problem #2 on one screenshot.) Insert it into the appropriate google slide. [br]***Geogebra will NOT save your work!!!!
Reflecting a Polygon
Read the directions and complete the problems below.
Step 1: Create a polygon with the following vertices [br] A(-4, 1), B(-2, 4), C(3, 1), and D(-1, -1) [br][br]Step 2: Decide which line you are reflecting over. [br] *If you are reflecting across either axis, move to step 4[br] *If you are reflecting over a line that is NOT an axis, the line must first be graphed. [br][br]Step 3: Graphing a line[br] a) Click[icon]/images/ggb/toolbar/mode_join.png[/icon] (3rd button). This tool will let you graph using two points. [br] b) Graph a line (in y = mx+b form) [br] c) The line can move by dragging either point. [br][br]Step 4: Reflecting[br] a) Click [icon]/images/ggb/toolbar/mode_mirroratline.png[/icon] (8th button) and choose reflecting about a line. [br] b) Click the polygon. [br] c) Click the line of reflection (axis or the line you've graphed) [br][br]Note: If you move points A, B, C, or D the corresponding image point will appropriately change as well. [br][br][b]Problem #1: R x-axis(ABCD) [/b] [br][br][b]Problem #2: R y=-1/2x +4(ABCD)[br][br][/b][b]*Perform each transformation within this applet. [br][br][/b]**Take a screen shot of your work (you will have problem #1 and problem #2 on one screenshot.) Insert it into the appropriate google slide. [br]***Geogebra will NOT save your work!!!!
Reflecting a polygon
Rotating a Polygon
Read the directions and complete the problems below.
Step 1: Create a polygon with the following vertices [br] A(-1, 2), B(1, 3), C(2, 5), and D(-2, 4) [br][br]Step 2: Decide which point you are rotating around. Use the point tool [icon]/images/ggb/toolbar/mode_point.png[/icon] (2nd button) to plot a point. Note: The point created needs to be bright blue. If you get a black dot or a light blue dot, delete it. Create a dot someplace else and move it to where you need it to be. [br][br]Step 3: Rotating [br] a) Click [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_mirroratline.png[/icon] (8th button) and choose rotating about a point [icon]/images/ggb/toolbar/mode_rotatebyangle.png[/icon][br] b) Click the polygon. [br] c) Click the center of rotation[br] d) Enter the angle of rotation. All angles will be entered a positive. Click counterclockwise or clockwise for the direction. [br][br]Note: If you move points A, B, C, or D the corresponding image point will appropriately change as well. [br][br][b]Problem #1: r(90, O )(ABCD) [/b] [br][br][b]Problem #2: r(-90, (5, 1)) (ABCD)[br][br][/b][b]*Perform each transformation within this applet. [br][br][/b]**Take a screen shot of your work (you will have problem #1 and problem #2 on one screenshot.) Insert it into the appropriate google slide. [br]***Geogebra will NOT save your work!!!!
Rotate a Polygon
Dilating a Polygon
Read the directions and complete the problems below.
Step 1: Create a polygon. This time, let's create a regular polygon. A regular polygon is a polygon is that has all sides equal and all angles equal. A square is an example of a regular polygon. [br] a) Click the polygon tool [icon]/images/ggb/toolbar/mode_polygon.png[/icon] and select regular polygon[icon]/images/ggb/toolbar/mode_regularpolygon.png[/icon]. [br] b) This tool will require you graph two points. [b](graph any two points)[/b][br] c) Then enter the number of vertices. [b](let's do 6 for this example)[/b][br][br]Step 2: Decide which is your center of dilation. Use the point tool [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_point.png[/icon] (2nd button) to plot a point, unless the point is a vertex of your polygon. [br] Note: The point created needs to be dark blue. If you get a black dot or a light blue dot, delete it. Create a dot someplace else and move it to where you need it to be. [br][br]Step 3: Dilating[br] a) Click [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_mirroratline.png[/icon] (8th button) and choose dilating from a point [icon]/images/ggb/toolbar/mode_dilatefrompoint.png[/icon][br] b) Click the polygon. [br] c) Click the center of dilation[br] d) Enter the scale factor. [br][br]Note: If you move the vertices, the corresponding image point will appropriately change as well. [br][br][b]Problem #1: D 5(ABCDEF) with (0, 0) as the center of dilation. [/b] [br][br][b]Problem #2:[/b][b]D 1/5 (ABCDEF) with as Point A. [/b][br][br][b]*Perform each transformation within this applet. [br][br][/b]**Take a screen shot of your work (you will have problem #1 and problem #2 on one screenshot.) Insert it into the appropriate google slide. [br]***Geogebra will NOT save your work!!!!
Dilating a Polygon
Problem #1
Problem #1: Use the polygon and your knowledge of geogebra to preform each transformation.
T<-3, 2> [math]\circ[/math] r(90, O) ([math]\bigtriangleup[/math]ABC) [br][br][br]Take a screen shot of your answer. Insert it into the appropriate google slide.
Preform the transformations.
Essential Understanding: Congruence Transformation
Essential Understanding
Two figures are [b]congruent[/b] if and only if there is a sequence of one or more rigid motions that maps one figure onto the other. [br][br]So what does that mean???[br][br]If you can perform a composition of transformations AND the shapes lay on top of each other AND are exactly the same, then they are congruent. [br][br]If you perform a composition of transformations AND the shapes don't lay perfectly on top of each other, then the shapes aren't congruent. [br][br]That's it! [br][br]For the two problems below, perform a composition of transformations. Take a screen shot of your work and insert it into the appropriate google slide. Are the shapes congruent?