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GeoGebraGeoGebra Classroom

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 Graphics View.

Construction Steps

1.Toolbar ImageCreate point A = (3, 1).
2.Toolbar ImageCreate line a: y = 0.
3.You might want to change the color of line a to see it on top of the x-axis.
4.Toolbar ImageReflect point A about line a to get its image A’. Hint: You might want to match the color of line a and point A’.
5.Toolbar ImageCreate line b: x = 0.
6.Toolbar ImageReflect point A about line b to get its image  A'1. Hint: You might want to match the color of line b and point A'1.

Try it yourself...

Construction Steps (continued)

7.Toolbar ImageSelect the Text tool and click in the upper part of the Graphics View. Enter Reflecting a point at the coordinate axes in the appearing dialog and click OK.
8.You might want to use the Style Bar in order to change the text formatting.
9.Toolbar ImageAdjust the position of the Text using the Move tool.
10.Fix the position of the Text so it can't be moved accidentally by using the Style Bar.
11.Toolbar ImageCreate a dynamic text showing the coordinates of point A.
Hint: Select the Text tool and click in the  Graphics View. In the appearing dialog, type the static part of your text A =. Afterwards, click on Advanced and select point A from the list on tab  Objects. Click OK when you are done.
12.Toolbar ImageInsert dynamic text that shows the coordinates of the reflected points A' and A'1.
13.Toolbar ImageZoom Out in order to show a larger part of the coordinate plane.
14.Toolbar ImageOpen the Properties dialog by using the Style Bar and set the distance of the grid lines to 1. Hint: On tabs xAxis and yAxis, check Distance and enter the distance 1.
15. Open the Style Bar and fix all texts so they can't be moved accidentally.
16. Close the Algebra View.

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.