Quiz — 659d9fa72c3c0_énoncé_Série-N°24( Rotations ).pdf

Question 1 sur 10 20:00

[{"id":69761,"question":"Quelle propriété est conservée par une rotation ?","option_a":"Les longueurs","option_b":"Les angles","option_c":"L'orientation","option_d":"Les deux premières réponses","option_e":"","option_f":"","bonne_reponse":"d","explication":"Une rotation est une isométrie, donc elle conserve les longueurs et les angles. Elle ne conserve pas l'orientation (sauf pour une rotation de 0° ou 360°).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"Les longueurs\", \"b\": \"Les angles\", \"c\": \"L'orientation\", \"d\": \"Le","_debug_options_count":4},{"id":69762,"question":"Une rotation de 90° dans le sens direct transforme le point A(2, 3) en A'. Quelles sont les coordonnées de A' ?","option_a":"(-3, 2)","option_b":"(3, -2)","option_c":"(-2, 3)","option_d":"(2, -3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant les formules de rotation : x' = 2*cos90° - 3*sin90° = -3 et y' = 2*sin90° + 3*cos90° = 2. Donc A'(-3, 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(-3, 2)\", \"b\": \"(3, -2)\", \"c\": \"(-2, 3)\", \"d\": \"(2, -3)\"}}","_debug_options_count":4},{"id":69763,"question":"Vrai ou Faux ? Une rotation de 180° est équivalente à une symétrie centrale.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une rotation de 180° autour d'un point O est effectivement équivalente à une symétrie centrale de centre O.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":69764,"question":"Quel est l'effet d'une rotation de 360° sur une figure ?","option_a":"La figure est inversée","option_b":"La figure est inchangée","option_c":"La figure est agrandie","option_d":"La figure est réduite","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une rotation de 360° ramène la figure à sa position initiale, donc elle est inchangée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"La figure est inversée\", \"b\": \"La figure est inchangée\", \"c\": \"","_debug_options_count":4},{"id":69765,"question":"Comment s'appelle le point fixe autour duquel une figure tourne lors d'une rotation ?","option_a":"Centre de symétrie","option_b":"Centre de rotation","option_c":"Pôle","option_d":"Origine","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le point fixe autour duquel une figure tourne est appelé le centre de rotation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Centre de symétrie\", \"b\": \"Centre de rotation\", \"c\": \"Pôle\", \"d","_debug_options_count":4},{"id":69766,"question":"Vrai ou Faux ? Une rotation de 45° dans le sens indirect transforme un carré en un losange.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une rotation conserve les longueurs et les angles, donc un carré reste un carré après rotation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":69767,"question":"Quelle est la mesure de l'angle de rotation qui transforme un triangle équilatéral en lui-même ?","option_a":"60°","option_b":"90°","option_c":"120°","option_d":"180°","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un triangle équilatéral a une symétrie de rotation de 120° (360°\/3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"60°\", \"b\": \"90°\", \"c\": \"120°\", \"d\": \"180°\"}}","_debug_options_count":4},{"id":69768,"question":"Vrai ou Faux ? Deux rotations successives de même centre et d'angles θ1 et θ2 équivalent à une seule rotation d'angle θ1 + θ2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La composition de deux rotations de même centre est une rotation d'angle égal à la somme des angles des deux rotations.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":69769,"question":"Quel est l'angle minimal pour qu'une rotation transforme un pentagone régulier en lui-même ?","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"72°","option_e":"","option_f":"","bonne_reponse":"d","explication":"Un pentagone régulier a une symétrie de rotation de 72° (360°\/5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"30°\", \"b\": \"45°\", \"c\": \"60°\", \"d\": \"72°\"}}","_debug_options_count":4},{"id":69770,"question":"Quelle transformation est équivalente à une rotation de 0° ?","option_a":"Une translation","option_b":"Une symétrie axiale","option_c":"L'identité","option_d":"Une homothétie","option_e":"","option_f":"","bonne_reponse":"c","explication":"Une rotation de 0° laisse la figure inchangée, ce qui correspond à l'identité.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Une translation\", \"b\": \"Une symétrie axiale\", \"c\": \"L'identité\"","_debug_options_count":4}]