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

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
00:12	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 Linetool from the tool bar
02:48	Click on the point D
02:49	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 ?
03:32	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
03:44	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
4:08	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 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
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
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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