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. |
Contributors and Content Editors
Madhurig, Minal, Mousumi, PoojaMoolya, Pratik kamble, Sandhya.np14