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Time Narration
0:00 Hello everybody.Welcome to this tutorial on Symmetrical Transformation in Geogebra
0:06 In this tutorial we will learn Symmetrical transformations such as
0:11 Line symmetry
0:12 Rotation symmetry
0:13 and also learn to

Enlarge figure with scale and position

0:17 We assume that you have the basic working knowledge of Geogebra
0:21 If not, For relevant tutorials, Please visit our website
0:26 To record this tutorial I am using

Ubuntu Linux OS Version 11.10

0:31 Geogebra Version
0:35 We will use the following Geogebra tools
0:37 Reflect Object about Line
0:39 Rotate Object around Point by Angle
0:42 Dilate object from a Point by Factor
0:45 Semicircle through Two points
0:47 Regular Polygon and
0:49 Perpendicular bisector
0:51 Definition of Transformation
0:53 Symmetrical transformation of a geometric figure is -
0:57 A change in its position, size or shape on a coordinate plane
1:02 Original figure is called 'Object'
1:04 Transformed figure is called 'Image'
1:07 Reflection symmetry
1:09 Is also called as Line symmetry
1:11 A type of symmetry where one half is the reflection of the other half
1:15 You could fold the image and have both halves match exactly
1:20 Line of Symmetry is the line over which the figure is reflected.
1:24 Let's Switch to GeoGebra window
1:27 Look on Dash home >>Media Apps>>Under Type >>Choose Education>> and Geogebra
1:37 For this tutorial I am closing the Algebric view
1:40 Click on Close button on Algebric view
1:47 Let's start with “Line of symmetry”
1:50 First let's construct an equilateral triangle.
1:53 Select “Regular Polygon” tool from the toolbar.
1:57 Click on drawing pad points 'A' ,'B', and enter 3 for the number of sides.
2:08 An equilateral triangle 'ABC' is drawn
2:11 Let's draw a perpendicular bisector to one of the sides of triangle
2:15 Select “Perpendicular Bisector Tool” and click on side AC
2:26 Select the Point tool and create a point inside the triangle.
2:31 Move the point D towards one of the vertices .
2:38 Right click on point D and select Trace ON
2:43 Select “Reflect Object about Line”tool from the tool bar
2:48 Click on the point D
2:49 This will highlight Point D
2:52 Click on perpendicular Bisector
2:55 This will produce reflected image D' on the other side of perpendicular bisector
3:01 'D is mirror image of point 'D'
3:04 Set Trace On for the point D'
3:08 Let us move the point D along the triangle using Move tool
3:11 Click on the first option under Move tool from the toolbar
3:22 Click on figure with the mouse.
3:25 Drag it tracing the triangle .
3:28 Now release the mouse button.
3:31 What do you notice ?
3:32 Here perpendicular bisector is the line of symmetry
3:36 D is the object and D' is the image
3:39 Let's reflect a semicircle about a line
3:43 Let's draw a semicircle
3:44 Click on the “Semicircle through Two points” tool Mark point E and then F
3:56 Click on segment Between two Points
4:02 Mark points G and H A line is drawn
4:06 Let's change the property of the line
4:08 Right click on the line Object properties Click on Style change Style
4:21 Select “Reflect Object about Line” tool from the toolbar
4:27 Click on the semicircle EF
4:31 Click on line GH
4:34 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
4:45 Let us save this file now
4:47 Click on “File”>> "Save As"
4:50 I will type the file name as "Line-symmetry" and click on “Save”
5:05 Next, let us learn to “Rotate the Object around a Point by Angle”
5:12 Definition of Rotation
5:15 A rotation is a transformation that turns a figure around a fixed center by an angle
5:21 If the figure appears unchanged, then the figure has rotation symmetry
5:29 You can rotate object at any degree measure Rotation can be clockwise and counterclockwise
5:39 Let's open a new Geogebra window
5:41 click on “File” >> New
5:47 Let us construct a square.
5:49 click on “Regular Polygon” tool from the toolbar
5:55 Click on the drawing pad
5:57 Mark points 'A' and 'B'
5:59 A dialog box opens
6:01 Click on OK
6:03 A square 'ABCD' is drawn
6:05 Click on “Rotate Object around a Point by Angle” tool
6:13 Click on the Square 'ABCD'
6:16 This will highlight the square
6:18 Next Click on any one of the vertices
6:20 I will click on 'A'
6:23 A dialog box opens
6:25 Type “60” in the Angle field
6:30 Select "°" from first drop down list
6:35 Select the option “clockwise”

Click on OK

6:40 This will rotate the square clockwise at the point of selection with the angle of 60°
6:44 The rotated image 'A`B`C` 'D' is formed
6:49 Let's move this figure aside using Move tool
7:00 Next, let's “Dilate or enlarge object from point by factor”
7:09 Dilation
7:11 Dilation or enlargement is a transformation
7:14 in which a figure is enlarged using a scale factor
7:23 Let's draw a triangle Using the “Polygon”tool
7:28 E , F , G click on E again to complete the triangle
7:36 Click on New point tool and
7:40 Mark a point 'H'
7:44 Click on “Dilate Object from Point by Factor” tool
7:51 Click on the triangle 'EFG'
7:54 This will highlight the triangle
7:55 Click on the point 'H'
7:57 A dialog box opens
8:00 Type value of 2 in the number field
8:04 Click on OK
8:09 This will dilate or enlarge the object twice
8:16 Click on Segment Between two Points, join points H,E,E'
8:33 join points H,G,G'
9:01 join points H,F,F'
9:15 Here you can see that H is the point of dilation
9:21 You can enlarge object as number of times as you wish, by typing the value of Factor
9:28 Let us save this file now
9:30 Click on “File”>> "Save As"
9:33 I will type the file name as "Dilate-triangle"
9:48 Click on “Save” with this we come to the end of this tutorial
9:55 Let's summarize
9:58 In this tutorial we learnt
10:00 Reflection about a line
10:02 Rotation of an object at a point
10:05 Enlargement of an object by a scale factor
10:09 As an assignment I would like you to
10:11 Draw a Pentagon
10:12 Use Regular Polygon tool to draw(Hint:sides=5)
10:17 Draw a Perpendicular bisector to one of the sides of the pentagon
10:21 Create a point in side the pentagon
10:25 Set trace On for the point
10:27 Get reflection of the point about the perpendicular bisector
10:31 Set trace On for the image point
10:34 Trace the pentagon to see if you have selected the correct line of symmetry
10:44 Rotate the original pentagon counter clockwise in 135° at a point
10:49 Dilate the pentagon at a point by the factor of 3
10:56 The assignment should look like this
11:03 Watch the video available at this URL
11:06 It summarises the Spoken Tutorial project
11:09 If you do not have good bandwidth,you can download and watch it
11:12 The Spoken Tutorial Project Team :

Conducts workshops using the spoken tutorials

11:17 Gives certificates to those who pass an online test
11:20 For more details, please write to

11:26 Spoken Tutorial Project is a part of the Talk to a Teacher project
11:29 It is supported by the National Mission on Education through ICT, MHRD, Government of India
11:35 More information on this Mission is available at this link.
11:39 This is Neeta Sawant from SNDT University Mumbai signing off.

Thanks for joining

Contributors and Content Editors

Madhurig, Minal, Mousumi, PoojaMoolya, Pratik kamble, Sandhya.np14