Schwerpunkt Dreieck Berechnen Beispiel Essay
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Unter Verwendung von als Mittelpunkt der Strecke lassen sich die Koordinaten des Schwerpunktes folgendermaßen angeben:
hat die Koordinaten und
In die Koordinaten von S eingesetzt liefert das die folgenden Werte für den Schwerpunkt :
Für den dreidimensionalen Fall lassen sich die Überlegungen analog führen, und für den Schwerpunkt gilt:
- Beipiel 1: Es sind die Koordinaten des Schwerpunktes S des Dreiecks mit den Punkten zu ermitteln.
Nach oben angegebener Formel ist:
Schwerpunkt in Vektordarstellung
Es seien die Ortsvektoren der Eckpunkte des Dreiecks , der Ortsvektor von (Halbierungspunkt von ) und der Ortvektor des Schwerpunktes S.
Dann gilt , und wegen erhält man:
- Beispiel 2: Man ermittle den Ortsvektor des Schwerpunktes S vom Dreieck mit den Punkten .