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

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.

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

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

What is a Spoken Tutorial

It summarises the Spoken Tutorial project

If you do not have good bandwidth,

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