# Geogebra/C2/Symmetrical-Transformation-in-Geogebra/English-timed

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 Time Narration 00:00 Hello everybody. Welcome to this tutorial on Symmetrical Transformation in Geogebra. 00:06 In this tutorial we will learn Symmetrical transformations such as: 00:11 Line symmetry Rotation symmetry 00:13 and also learn to enlarge figure with scale and position. 00:17 We assume that you have the basic working knowledge of Geogebra. 00:21 If not, for relevant tutorials, please visit our website. 00:26 To record this tutorial, I am using Ubuntu Linux OS Version 11.10, 00:31 Geogebra Version 3.2.47.0. 00:35 We will use the following Geogebra tools: 00:37 Reflect Object about Line 00:39 Rotate Object around Point by Angle 00:42 Dilate object from a Point by Factor 00:45 Semicircle through Two points 00:47 Regular Polygon and 00:49 Perpendicular bisector 00:51 Definition of Transformation- 00:53 Symmetrical transformation of a geometric figure is: 00:57 A change in its position, size or shape on a coordinate plane. 01:02 Original figure is called Object. 01:04 Transformed figure is called Image. 01:07 Reflection symmetry: 01:09 Is also called as Line symmetry. 01:11 A type of symmetry where one half is the reflection of the other half. 01:15 You could fold the image and have both halves match exactly. 01:20 Line of Symmetry is the line over which the figure is reflected. 01:24 Let's switch to Geogebra window. 01:27 Look on Dash home >> Media Apps >> under Type >> choose Education >> and Geogebra. 01:37 For this tutorial, I am closing the Algebric view. 01:40 Click on Close button on Algebric view. 01:47 Let's start with Line of symmetry. 01:50 First, let's construct an equilateral triangle. 01:53 Select Regular Polygon tool from the toolbar. 01:57 Click on drawing pad points A ,B, and enter 3 for the number of sides. 02:08 An equilateral triangle ABC is drawn. 02:11 Let's draw a perpendicular bisector to one of the sides of triangle. 02:15 Select Perpendicular Bisector Tool and click on side AC. 02:26 Select the Point tool and create a point inside the triangle. 02:31 Move the point D towards one of the vertices . 02:38 Right click on point D and select Trace On. 02:43 Select Reflect Object about Line tool from the tool bar. 02:48 Click on the point D.This will highlight point D. 02:52 Click on Perpendicular Bisector. 02:55 This will produce reflected image D' on the other side of perpendicular bisector. 03:01 D' is mirror image of point D. 03:04 Set Trace On for the point D. 03:08 Let us move the point D along the triangle, using Move tool. 03:11 Click on the first option under Move tool from the toolbar. 03:22 Click on figure with the mouse. 03:25 Drag it tracing the triangle . 03:28 Now release the mouse button. 03:31 What do you notice ? Here perpendicular bisector is the line of symmetry. 03:36 D is the object and D' is the image. 03:39 Let's reflect a semicircle about a line. 03:43 Let's draw a semicircle.Click on the Semicircle through Two points tool. Mark point E and then F. 03:56 Click on segment between two points. 04:02 Mark points G and H. A line is drawn. 04:06 Let's change the property of the line. 04:08 Right click on the line, Object Properties. Click on Style, change Style. 04:21 Select Reflect Object about Line tool from the toolbar. 04:27 Click on the semicircle EF. 04:31 Click on line GH. 04:34 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. 04:45 Let us save this file now. 04:47 Click on File Save As. 04:50 I will type the file name as Line-symmetry and click on Save. 05:05 Next, let us learn to Rotate the Object around a Point by Angle. 05:12 Definition of Rotation- 05:15 A rotation is a transformation that turns a figure around a fixed center by an angle. 05:21 If the figure appears unchanged then the figure has rotation symmetry. 05:29 You can rotate object at any degree measure. Rotation can be clockwise and counterclockwise. 05:39 Let's open a new Geogebra window. 05:41 click on File New. 05:47 Let us construct a square. 05:49 click on Regular Polygon tool from the toolbar. 05:55 Click on the drawing pad. 05:57 Mark points A and B. 05:59 A dialog box opens. 06:01 Click on OK. 06:03 A square ABCD is drawn. 06:05 Click on Rotate Object around a Point by Angle tool. 06:13 Click on the Square ABCD. 06:16 This will highlight the square. 06:18 Next Click on any one of the vertices. 06:20 I will click on A. 06:23 A dialog box opens. 06:25 Type 60 in the Angle field 06:30 Select °(Degree) from first drop down list. 06:35 Select the option clockwise. Click on OK. 06:40 This will rotate the square clockwise at the point of selection, with the angle of 60°. 06:44 The rotated image A`B`C`D` is formed. 06:49 Let's move this figure aside using Move tool. 07:00 Next, let's dilate or enlarge object from point by factor. 07:09 Dilation: 07:11 Dilation or enlargement is a transformation 07:14 in which a figure is enlarged using a scale factor. 07:23 Let's draw a triangle using the Polygontool, 07:28 E , F , G. Click on E again to complete the triangle. 07:36 Click on New Point tool and 07:40 mark a point H. 07:44 Click on Dilate Object from Point by Factor tool. 07:51 Click on the triangle EFG. 07:54 This will highlight the triangle. 07:55 Click on the point 'H'. 07:57 A dialog box opens. 08:00 Type value of 2 in the number field. 08:04 Click on OK. 08:09 This will dilate or enlarge the object twice. 08:16 Click on segment between two Points, join points H,E,E'. 08:33 join points H,G,G'. 09:01 join points H,F,F'. 09:15 Here, you can see that H is the point of dilation. 09:21 You can enlarge object as many number of times as you wish, by typing the value of Factor. 09:28 Let us save this file now. 09:30 Click on File >> Save As. 09:33 I will type the file name as Dilate-triangle. 09:48 Click on Save. With this we come to the end of this tutorial. 09:55 Let's summarize. 09:58 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.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 inside 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 summarizes 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 contact@spoken-tutorial.org. 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.