T.P.3 - Une nouvelle transformation

1) Dans la fenêtre ci-dessous, placer trois points A, B et C.[br]2) Construire le triangle ABC en utilisant l'icône [img]data:image/png;base64,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[/img].[br]3) Placer un point O à l'extérieur du triangle.[br]4) Activer l'icône homothétie [img]data:image/png;base64,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[/img] et cliquer sur le triangle ABC puis sur le point O et choisir 2 comme rapport.[br]Tu obtiens ainsi le triangle A'B'C', image du triangle ABC par l'homothétie de centre O et de rapport 2.
5) Déplacer le point O pour observer ce qui se passe. Modifier également la position des points A, B et C.[br]6) Que remarques-tu sur les côtés du triangle A'B'C' par rapport à ceux de ABC ?[br](longueur, position... on pourra utiliser les icônes [img]data:image/png;base64,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[/img] et [img]data:image/png;base64,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[/img])
7) Si on superpose le point O à l'un des sommets du triangle ABC, quelle configuration retrouve-t-on ?
8) Sur la même figure, refaire les questions 4), 5) et 6) en prenant un rapport entre 0 et 1.[br]9) Qu'est-ce qui change dans ce cas ?
10) Une homothétie est une transformation géométrique qui produit des agrandissements et des réductions. [br]Es-tu d’accord avec cette définition ? Explique ton choix.
11) Que se passe-t-il lorsqu'on choisit un rapport négatif ?[br]On pourra tracer les droites passant par le point O et les sommets du triangle ABC pour mieux observer.
12) Quelle transformation retrouve-ton lorsque le rapport de l'homothétie est égal à -1 ?
Close

Information: T.P.3 - Une nouvelle transformation