Displaying the Coordinates of Reflected Points

Task
Create an interactive activity that allows to explore the coordinates of reflected points by inserting static and dynamic text into the [img]https://www.geogebra.org/wiki/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i].
Construction Steps
[table] [tr] [td]1.[/td] [td][icon]/images/ggb/toolbar/mode_point.png[/icon][/td] [td]Create point [code]A = (3, 1)[/code].[/td][/tr][tr][td]2.[/td] [td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td] [td]Create line [code]a: y = 0[/code].[/td][/tr][tr] [td]3.[/td] [td][img]https://www.geogebra.org/wiki/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/32px-Stylingbar_icon_graphics.svg.png[/img][/td] [td]You might want to change the color of line [i]a[/i] to see it on top of the [i]x[/i]-axis.[/td][/tr] [tr] [td]4.[/td] [td][icon]/images/ggb/toolbar/mode_mirroratline.png[/icon][/td] [td]Reflect point [i]A[/i] about line [i]a[/i] to get its image [i]A’[/i].[br][u]Hint[/u]: You might want to match the color of line [i]a[/i] and point [i]A’[/i].[/td][/tr] [tr] [td]5.[/td] [td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td] [td]Create line [code]b: x = 0[/code].[/td][/tr] [tr] [td]6.[/td] [td][icon]/images/ggb/toolbar/mode_mirroratline.png[/icon][/td] [td]Reflect point [i]A[/i] about line b to get its image [i][/i] [i]A'[sub]1[/sub][/i].[br][u]Hint[/u]: You might want to match the color of line [i]b[/i] and point [i]A'[sub]1[/sub][/i].[code][/code][br][/td][/tr][/table]
Try it yourself...
Construction Steps (continued)
[table][tr][td]7.[/td][td][icon]/images/ggb/toolbar/mode_text.png[/icon][/td][td]Select the [i]Text [/i]tool and click in the upper part of the [img]https://www.geogebra.org/wiki/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i]. Enter [code]Reflecting a point at the coordinate axes[/code] in the appearing dialog and click [i]OK[/i].[/td][/tr][tr][td]8.[/td][td][img]https://www.geogebra.org/wiki/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/32px-Stylingbar_icon_graphics.svg.png[/img][/td][td]You might want to use the [i]Style Bar[/i] in order to change the text formatting.[/td][/tr][tr][td]9.[/td][td][icon]/images/ggb/toolbar/mode_move.png[/icon][/td][td]Adjust the position of the [i]Text [/i]using the [i]Move [/i]tool.[/td][/tr][tr][td]10.[/td][td][img]https://www.geogebra.org/wiki/uploads/thumb/9/92/Stylingbar_object_unfixed.svg/32px-Stylingbar_object_unfixed.svg.png[/img][/td][td]Fix the position of the [i]Text [/i]so it can't be moved accidentally by using the [img]https://www.geogebra.org/wiki/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/16px-Stylingbar_icon_graphics.svg.png[/img] [i]Style Bar[/i].[/td][/tr][tr][td]11.[/td][td][icon]/images/ggb/toolbar/mode_text.png[/icon][/td][td]Create a dynamic text showing the coordinates of point [i]A[/i].[br][/td][/tr][tr][td][/td][td][/td][td][u]Hint[/u]: Select the [img]https://www.geogebra.org/wiki/uploads/thumb/1/14/Mode_text.svg/16px-Mode_text.svg.png[/img] [i]Text [/i]tool and click in the [img]https://www.geogebra.org/wiki/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i]. In the appearing dialog, type the static part of your text [code]A =[/code]. Afterwards, click on [i]Advanced [/i]and select point [i]A[/i] from the list on tab [img]https://wiki.geogebra.org/uploads/thumb/4/4e/Geogebra-logo-elipse.svg/16px-Geogebra-logo-elipse.svg.png[/img] [i]Objects[/i]. Click [button_small]OK[/button_small] when you are done.[br][/td][/tr][tr][td]12.[/td][td][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_text.png[/icon][/td][td]Insert dynamic text that shows the coordinates of the reflected points [i]A'[/i] and [i]A'[sub]1[/sub][/i].[/td][/tr][tr][td]13.[/td][td][icon]/images/ggb/toolbar/mode_zoomout.png[/icon][/td][td][i]Zoom Out[/i] in order to show a larger part of the coordinate plane.[/td][/tr][tr][td]14.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/3/30/Menu-options.svg/120px-Menu-options.svg.png[/icon][/td][td]Open the [i]Properties dialog[/i] by using the [img]https://www.geogebra.org/wiki/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/16px-Stylingbar_icon_graphics.svg.png[/img] [i]Style Bar[/i] and set the distance of the grid lines to 1.[br][u]Hint[/u]: On tabs [i]xAxis[/i] and [i]yAxis[/i], check [i]Distance [/i]and enter the distance 1. [/td][/tr][tr][td]15.[/td][td][img]https://www.geogebra.org/wiki/uploads/thumb/9/92/Stylingbar_object_unfixed.svg/32px-Stylingbar_object_unfixed.svg.png[/img][br][/td][td]Open the [img]https://www.geogebra.org/wiki/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/16px-Stylingbar_icon_graphics.svg.png[/img] [i]Style Bar[/i] and fix all texts so they can't be moved accidentally.[/td][/tr][tr][td]16.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/6/6c/Stylingbar_icon_algebra.svg/32px-Stylingbar_icon_algebra.svg.png[/img][br][/td][td]Close the [img]https://www.geogebra.org/wiki/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i].[/td][/tr][/table]
Task
Come up with instructions to guide your students towards discovering the relation between the coordinates of the original and the reflected points which could be provided along with the dynamic figure you just created.
Close

Information: Displaying the Coordinates of Reflected Points