M3.V.15b A2 ABL Problem Abstand Punkt-Gerade

[img]https://mategnu.de/bilder/banner/Arbeitsblatt_Lsg.png[/img]
Problem
Gegeben sind ein Punkt P und eine Gerade d in einem räumlichen Koordinatensystem. [br]Der Punkt liegt nicht auf der Geraden g.[br]Wie kann man vorgehen, um den Abstand des Punktes P zur Geraden g zu bestimmen?[br][img]data:image/png;base64,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[/img]
Aufgabe 1: Ideensammlung
Sammeln Sie möglichst viele verschiedene Lösungsideen zur Abstandsbestimmung.[br][i][br]Hinweis: Welche geometrischen Objekte (z. B. Punkt, Vektor, Gerade, Ebene, Dreieck, Viereck, Kugel) können dabei helfen?[/i]
Aufgabe 2: Vorgehen zu einer Idee
Entwickeln Sie für eine der Ideen ein konkretes Vorgehen und beschreiben Sie dieses mit allen notwendigen Schritten.[br][br][i]Die Ideenkarten können Ihnen bei der Ausarbeitung [i]helfen[/i].[/i]
Ideenkarten
Aufgabe 3: Berechnung
Berechnen Sie mit diesem Vorgehen den Abstand des Punktes P=(1,2,3) zu der Geraden g:[br][img]data:image/png;base64,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[/img]
GeoGebra 3D
[i][u]Quellen: [/u][br][i]Susanne Digel und Jürgen Roth.[br]Idee: Frohn, D. & Salle, A. (2020). Wie finde ich den richtigen Abstand? Das Prinzip der Orientierung an Grundvorstellungen. Mathematik lehren, 223, 32–36[/i].[/i]
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Information: M3.V.15b A2 ABL Problem Abstand Punkt-Gerade