View source for Geogebra/C2/Symmetrical-Transformation-in-Geogebra/English

Title of script: Symmetrical Transformation in Geogebra

Author: Neeta Sawant

Keywords:  Symmetry-line and Rotation, Reflect Object about Line, Rotate Object around Point by Angle,  Dilate object from a Point by Factor,  Semicircle through Two points,  Dilation, Set trace On, video tutorial

[http://spoken-tutorial.org/wiki/index.php/File:Symmetrical-transformation.tar.gz Click here for Slides]

{|border =1
!Visual Cue
!Narration
|-
||Slide Number 1
||Hello everybody. 

Welcome to this tutorial on Symmetrical Transformation in Geogebra

|-
||Slide  Number 2
Learning Objectives

||In this tutorial we will learn  Symmetrical transformations such as 

* Line symmetry

* Rotation symmetry

and also learn to

* Enlarge figure with scale and position 

|-
||Slide  Number 3
Pre-requisites
||We assume that you have the basic working knowledge of Geogebra

If not, 
For relevant tutorials on Geogebra.

Please visit our website

http://spoken-tutorial.org
|-
||Slide Number 4

System Requirement
||To record this tutorial I am using  

Ubuntu Linux OS Version  11.10 

Geogebra Version 3.2.47.0 
|-
||Slide Number 5
 
GeoGebra Tools  used in this tutorial
||We will use the following Geogebra tools

* Reflect Object about Line

* Rotate Object around  Point by Angle

* Dilate object from a Point by Factor

* Semicircle through Two points 

* Regular Polygon and 

* Perpendicular bisector
|-
||slide Number 6
Definition of Transformation
|| 
Symmetrical transformation of a geometric figure is -

A change in its position, size or shape on a coordinate plane

Original figure is called 'Object'

Transformed figure is called 'Image' 
|-

||Slide Number 7
Reflection symmetry 
||Reflection symmetry 

Is also called as Line symmetry

A type of symmetry where one half is the reflection of the other half  

You could fold the image and have both halves match exactly
|-
||Switch to GeoGebra window
Dash  home >>Media Apps>>Under Type       >>Education>>Geogebra
||Let's Switch to GeoGebra window

Dash home >>Media Apps>>Under Type     >>Choose Education>> and  Geogebra

|-
||Click on Close button on Algebric view 
||
For this tutorial I am closing the Algebric view

Click on Close button on Algebric view 
|-
||
||Let's start with “Line of symmetry”
|-
||Click on “Polygon” tool >>  To Construct  a triangle
|| First let's  construct  an equilateral triangletriangle  
 
Select  “Regular Polygon” tool from toolbar. 
 |-
||Click on drawing pad
Points 'A' ,'B' >>enter 3
click Ok
||
Click on drawing pad  points 'A' ,'B', and enter 3 for the number of sides.  
 
An equilateral  triangle  'ABC' is drawn
|-
||Select “Perpendicular Bisector Tool” >> click on side AC
||Let's draw a  perpendicular bisector to one of the sides of the triangle

Select “Perpendicular Bisector Tool” and click on side AC
|-
||Select the Point tool >> create a point D 

Right click on point D >> select Trace ON 

Click on Reflect Object about Line

||Select the Point tool and  create a point D .

Move the point D towards  one of the vertices .

Right click on point D and select Trace ON 

Select “Reflect Object about Line”tool from the tool bar
|-
||Click on the Point D 
||Click on the Point D 

This will highlight  Point D
|-
||Click on perpendicular Bisector
||Click on perpendicular Bisector

This will produce  reflected image D' on the other side of perpendicular bisector 
|-
||
|| 'D is mirror image of point  'D'
Set Trace On for the point D'

|-

||
||Let us move the point D along the triangle using  Move tool
|-
||Click on the “Move” tool
||Click on the first option under Move tool from the toolbar
|-
||Drag the object 
||Click on  figure with the mouse.

Drag it tracing the triangle .  

Now release the mouse button.

What do you notice ? 

Here perpendicular bisector is the line of symmetry

D is the object and D' is the image
|-
||
||Let's reflect a semicircle about a line 
|-
||Click on the “Semicircle  through Two points” tool >>Mark points E and F
|| Let's draw a semicircle
Click on the “Semicircle  through Two points” tool Mark point  E and   F 
|-
|| Click on Segement Between two points>> Draw a line GH
|| Click on segment Between two Points 
Mark points G and H 
A line is drawn
|-
||Right click on line GH>>Object properties >>Click on Style>>change Style
||Let's change the object properties 
Right click on line GH
Click on Object properties 
Click on Style
change Style
|-
||Click on Reflect Object about Line 
||Select “Reflect Object about Line” tool from the toolbar
|-
||Click on the semicircle EF
||Click on the semicircle EF
This will highlight the semicircle EF
|-
||Click on line GH
||Click on line  GH
This will produce the reflected image E'F' on the other side of line GH
What does the figure look like now ?
It looks like a circle
|-
||Click on "Save As" >> type " Line-symmetry " in file 
name >> click on save
||Let us save this file now
Click on  “File”>>  "Save As"

I will type the file name as "Line-symmetry" and click on “Save”
|-
||
||Next, let us learn  “Rotate Object around  a Point by  Angle”
|-
||Slide Number 9
Definition of Rotation 
||Definition of Rotation 
A rotation is a transformation that turns a figure around a fixed center by an angle

If the figure appears unchanged, then the figure has rotation symmetry

You can rotate object at any degree measure
Rotation can be clockwise and counterclockwise
|-
||Click on “File” >> New
||Let's open a new Geogebra window

click on “File” >> New 
|-
||Click on “Polygon” tool >>  To Construct  a Square 
||Let us  construct a square  'ABCD'
 
click on  “Regular Polygon” tool from the toolbar
|-
||Click on drawing pad and mark points 'A' and 'B'
||Click on the drawing pad 

Mark points 'A' and 'B'
|-
||A dialog box  opens
Click OK
||A dialog box  opens
Click on OK 

A square 'ABCD' is drawn
|-
||Click on Rotate Object around  a Point by Angle 
||Click on “Rotate Object around  a Point by Angle” tool
|-
||Click on the Square  'ABCD'
||Click on the Square 'ABCD' 

This will highlight the square 
|-
||Click on the point 
||Next Click on any one of the vertices
I will click on 'A'
|-
||A dialog  box opens 
||A dialog  box opens 
|-
||Type "60" in  Angle field
||Type “60” in the Angle field
|-
||Select "°" from first drop down list
||Select "°" from  first drop down list
|-
||Select the option "Clockwise" 
||Select the option “clockwise”
|-
||Click on OK
||Click on OK
This will rotate the square clockwise at the point of selection with the angle of 60

The rotated image 'A`B`C` 'D' is formed
|-
||
||Let's move this figure aside using Move tool
|-
||
||Next, let's “Dilate or enlarge object from point by factor” 
|-
||Slide Number 10 
Dilation 
||Dilation
* Dilation or enlargement is a transformation 

* in which a figure is enlarged using a scale factor
|-
||Draw a triangle 'ABC'
||Let's draw a  triangle Using the “Polygon”tool 

E , F , G click on E again to complete the triangle
|-
||Click on New point tool>>Mark point 'H'
||Click on New point tool and
Mark a point 'H'
|-

||Click on  Dilate Object from Point by Factor tool
||Click on   “Dilate Object from Point by Factor” tool
|-
||Click on triangle 'EFG
||Click on the triangle 'EFG' 

This will highlight the triangle 
|-
||Click on a point 'H'
||Click on the point 'H'

|-
||A dialog box opens 
||A dialog box opens 
|-
||Type "2">>click  OK
||Type 2 in  the number field 
 
Click on OK
|-
||
||This will dilate or enlarge the object twice 
|-
||Click on Segement Between two Points >> join points
|| Click on Segement Between two Points tool
join points H,E,E'
join points H,G,G'
join points H,F,F'

|-
||
||Here you can see that H is the point of dilation

You can enlarge  object as number of times as you wish, 
by typing the value of Factor

|-
||Click on "Save As" >> type " Dilate-triangle " in file 
name >> click on save
||Let us save this file now 
Click on  “File”>>  "Save As"

I will type the file name as "Dilate-triangle" 

Click on “Save”
with this we come to the tutorial
|-
||Slide Number 11
Summary
||Let's summarize 

In this tutorial we learnt 
* Reflection about a line 

* Rotation of an object at a point

* Enlargement of an object by a scale factor

|-
||Slide Number 12
Assignment
||

As an assignment I would like you to 

Draw a Pentagon 

Use Regular Polygon tool to draw(Hint:sides=5)

Draw a Perpendicular bisector to one of the sides of the pentagon

Create a point in side the pentagon 

Set trace On for the point

Get reflection of the point about the perpendicular bisector

Set trace On for the image point

Trace the pentagon to see if you have selected the 
correct line of symmetry 

Rotate the original pentagon counter clockwise in 135° at a point 

Dilate  the pentagon at a point by the factor of 3
|-
||Show the output of the Assignment
||The assignment  should look like this
|-
||Slide number 13
Acknowledgement
||
Watch the video available at 

http://spoken-tutorial.org/ 

What is a Spoken Tutorial 

It summarises the Spoken Tutorial project 

If you do not have good bandwidth, 

you can download and watch it 
|-
||
||The Spoken Tutorial Project Team :

Conducts workshops using spoken tutorials 

Gives certificates to those who pass an online test 

For more details, please write to

contact@spoken-tutorial.org
|-
||
||
Spoken Tutorial Project is a part  of the Talk to a Teacher project 

It is supported by the National Mission on Education through ICT, MHRD, Government of India 

More information on this Mission is available at http://spoken-tutorial.org/NMEICT-Intro 

This is Neeta Sawant  from SNDT Mumbai  signing off.

Thanks for joining