Achsenspiegelung an Ursprungsgeraden: Abbildungsmatrix

Der Punkt [color=#0000ff][b]A(x|y)[/b][/color] wird durch Achsenspiegelung an der [color=#ff0000]Ursprungsgeraden s[/color] auf den Punkt [color=#ff00ff][b]A'(x'|y')[/b][/color] abgebildet.[br][br][img]data:image/png;base64,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[/img][br][br]Die [color=#ff0000]Spiegelachse s[/color] bildet mit der positiven x-Achse den Winkel mit dem [color=#ff0000]Maß α[/color].[br][br][u][b]Ziel: [/b]Matrixform der Abbildungsgleichung der Achsenspiegelung an einer Ursprungsgeraden.[/u][br][br][br]Die Zeichnung und die folgenden Schritte helfen dir:[br][br][list][*]Die Zeichnung zeigt die Abbildung von A auf A'.[/*][*]Die Zeichnung ist ergänzt durch 2 rechtwinklige Dreiecke [color=#0000ff]OQA[/color] und [color=#ff00ff]ORA'[/color].[/*][*]Die Katheten der Dreiecke sind entsprechend der Punktkoordinaten beschriftet.[/*][*]Die Hypotenusen der Dreiecke sind gleich lang (z LE).[/*][/list]
Schritt 1:
Betrachte das [color=#0000ff][b]Dreieck OQA[/b][/color].[br][i](Bearbeite die Schritte 1 bis 4 in deinem Heft [icon]/images/ggb/toolbar/mode_pen.png[/icon].)[/i][br][list][*]Stelle eine Gleichung für [math]cos\;\varphi[/math] und eine Gleichung für [math]sin\;\varphi[/math] auf.[/*][*]Lösen anschließend nach x bzw. y auf.[/*][/list]
Schritt 2:
Betrachte das [b][color=#ff00ff]Dreieck ORA'[/color][/b].[br][list][*]Stelle eine Gleichung für [math]cos\;(2 \alpha - \varphi)[/math] und eine Gleichung für [math]sin\;(2 \alpha - \varphi)[/math] auf.[/*][*]Löse anschließend nach x' bzw. y' auf.[/*][*]Wende die Additionstheoreme auf [math]cos\;(2 \alpha - \varphi)[/math] bzw. [math]sin\;(2 \alpha - \varphi)[/math] an.[/*][*]Multipliziere aus.[/*][/list]
Schritt 3:
Die Terme [math]z\cdot cos\, \varphi[/math] bzw. [math]z\cdot sin\, \varphi[/math] kommen in den Ergebnissen beider Schritte vor.[br]Setze die Ergebnisse aus Schritt 1 in die Ergebnisse aus Schritt 2 ein. Du erhältst die Abbildungsgleichung in Koordinatenform.
Schritt 4:
Schreibe die Abbildungsgleichung in Matrixform.
Musteraufgabe
Der Punkt [color=#0000ff][b]A(5|1)[/b][/color] wird durch Achsenspiegelung an der [color=#ff0000]Ursprungsgeraden s: [math]y=\frac{2}{3}x[/math][/color] auf den Punkt [color=#ff00ff][b]A'(x'|y')[/b][/color] abgebildet. Berechne die Koordinaten des Bildpunktes A'. ([math]x,y\in\mathbb{R}[/math])[br][br][img]data:image/png;base64,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[/img]
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Information: Achsenspiegelung an Ursprungsgeraden: Abbildungsmatrix