Transformations géométriques : isométries et homothéties

Question 1 sur 10 10:00

[{"id":60677,"question":"Quelle transformation conserve les distances et les angles ?","option_a":"Homothétie","option_b":"Isométrie","option_c":"Projection","option_d":"Réflexion","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une isométrie est une transformation qui conserve les distances et les angles, contrairement aux autres options.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60678,"question":"Une homothétie de rapport 2 agrandit-elle ou réduit-elle une figure ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une homothétie de rapport 2 agrandit la figure car |2| \u003E 1. Si le rapport est entre -1 et 1 (exclu), la figure est réduite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60679,"question":"Quelle est l'image d'un point A(3, 4) par une translation de vecteur (2, -1) ?","option_a":"A'(5, 3)","option_b":"A'(1, 5)","option_c":"A'(5, 5)","option_d":"A'(1, 3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'image d'un point (x, y) par une translation de vecteur (a, b) est (x+a, y+b). Ici, (3+2, 4-1) = (5, 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60680,"question":"Une symétrie centrale est-elle une isométrie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une symétrie centrale conserve les distances et les angles, donc c'est une isométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60681,"question":"Quel est le rapport d'une homothétie qui réduit une figure de moitié ?","option_a":"2","option_b":"-2","option_c":"0.5","option_d":"-0.5","option_e":"","option_f":"","bonne_reponse":"C","explication":"Un rapport de 0.5 réduit la figure de moitié. Le signe négatif indique une inversion de sens.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60682,"question":"Quelle transformation fait tourner une figure autour d'un point fixe ?","option_a":"Translation","option_b":"Rotation","option_c":"Homothétie","option_d":"Symétrie axiale","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une rotation fait tourner une figure autour d'un point fixe appelé centre de rotation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60683,"question":"L'image d'un segment [AB] par une symétrie axiale est-elle parallèle à [AB] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'image d'un segment par une symétrie axiale est un segment parallèle à l'original, mais de sens opposé.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60684,"question":"Quelle est la nature de la transformation qui associe à tout point M son image M' telle que MM' = 2MA ?","option_a":"Translation","option_b":"Homothétie de rapport 2","option_c":"Rotation","option_d":"Symétrie centrale","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette transformation est une homothétie de rapport 2 centrée en A, car MM' = 2MA.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60685,"question":"Une homothétie de rapport -1 est-elle équivalente à une symétrie centrale ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une homothétie de rapport -1 est équivalente à une symétrie centrale, car elle inverse les distances et les angles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60686,"question":"Quelle transformation conserve les angles mais pas nécessairement les distances ?","option_a":"Isométrie","option_b":"Homothétie","option_c":"Projection","option_d":"Translation","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une homothétie conserve les angles mais modifie les distances selon le rapport donné.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]