Proportionnalité

Pour aller plus loin (Ancien programme) - Mathématiques 5e

Exemple d'exercice parmi les 105 exercices du chapitre

On considère la figure modèle suivante :

Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.

A.

{"path": [[[[0.6224449714253065, 4.961104943210469], [0.0, 0.0], [4.961104943210469, -0.6224449714253065], [5.583549914635776, 4.338659971785162], [0.6224449714253065, 4.961104943210469]]], [[[0.0, 0.0], [0.06224449714253065, 0.49611049432104687], [0.5583549914635775, 0.4338659971785162], [0.49611049432104687, -0.06224449714253065], [0.0, 0.0]]], [[[2.7917749573178874, 2.169329985892581], [2.430219959669124, 2.6346258121122292], [1.9649241334494763, 2.2730708144634657], [2.3264791310982393, 1.8077749882438177], [2.7917749573178874, 2.169329985892581]]]], "init": {"range": [[-1.0, 6.583549914635776], [-1.6224449714253066, 5.961104943210469]], "scale": [45, 45]}, "line": [[[0.45584448477215866, 2.294434141117375], [0.16660048665314786, 2.6666708020930936]], [[0.6224449714253065, 4.961104943210469], [0.0, 0.0], {"subtype": "segment"}], [[2.6666708020930936, -0.16660048665314786], [2.294434141117375, -0.45584448477215866]], [[0.0, 0.0], [4.961104943210469, -0.6224449714253065], {"subtype": "segment"}], [[5.127705429863616, 2.044225830667787], [5.416949427982627, 1.6719891696920688]], [[4.961104943210469, -0.6224449714253065], [5.583549914635776, 4.338659971785162], {"subtype": "segment"}], [[2.9168791125426816, 4.50526045843831], [3.2891157735184002, 4.794504456557321]], [[5.583549914635776, 4.338659971785162], [0.6224449714253065, 4.961104943210469], {"subtype": "segment"}], [[0.6224449714253065, 4.961104943210469], [4.961104943210469, -0.6224449714253065], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.583549914635776, 4.338659971785162], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
B.

{"path": [[[[-1.0625905654760572, -1.6943734211091936], [0.0, 0.0], [-1.9661167593358408, -0.3664026318938386], [-3.028707324811898, -2.0607760530030323], [-1.0625905654760572, -1.6943734211091936]]], [[[-1.514353662405949, -1.0303880265015162], [-1.4390598129176337, -1.1410522589361292], [-1.3283972952254892, -1.0657558892417878], [-1.4036911447138045, -0.955091656807175], [-1.514353662405949, -1.0303880265015162]]]], "init": {"range": [[-4.028707324811898, 1.0], [-3.0607760530030323, 1.0]], "scale": [45, 45]}, "line": [[[-0.5523547112591332, -0.7552879110017552], [-0.5102358542169241, -0.9390855101074385]], [[-0.5877743967750018, -0.8117670250387283], [-0.5456555397327927, -0.9955646241444116]], [[-1.0625905654760572, -1.6943734211091936], [0.0, 0.0], {"subtype": "segment"}], [[-1.0363830771121498, -0.2609532646772905], [-0.9297336822236909, -0.1054493672165481]], [[-0.9708447540248496, -0.24873963903421964], [-0.8641953591363906, -0.09323574157347725]], [[0.0, 0.0], [-1.9661167593358408, -0.3664026318938386], {"subtype": "segment"}], [[-2.476352613552765, -1.3054881420012772], [-2.518471470594974, -1.1216905428955937]], [[-2.4409329280368963, -1.249009027964304], [-2.4830517850791054, -1.0652114288586205]], [[-1.9661167593358408, -0.3664026318938386], [-3.028707324811898, -2.0607760530030323], {"subtype": "segment"}], [[-1.9923242476997483, -1.7998227883257418], [-2.098973642588207, -1.9553266857864844]], [[-2.057862570787049, -1.8120364139688128], [-2.1645119656755076, -1.9675403114295553]], [[-3.028707324811898, -2.0607760530030323], [-1.0625905654760572, -1.6943734211091936], {"subtype": "segment"}], [[-1.0625905654760572, -1.6943734211091936], [-1.9661167593358408, -0.3664026318938386], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [-3.028707324811898, -2.0607760530030323], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
C.

{"path": [[[[1.023935120889313, 2.8198505045851965], [0.0, 0.0], [4.6997508409753275, -1.7065585348155219], [5.723685961864641, 1.1132919697696748], [1.023935120889313, 2.8198505045851965]]], [[[0.0, 0.0], [0.17065585348155218, 0.46997508409753275], [0.640630937579085, 0.29931923061598054], [0.46997508409753275, -0.17065585348155218], [0.0, 0.0]]]], "init": {"range": [[-1.0, 6.723685961864641], [-2.706558534815522, 3.8198505045851965]], "scale": [45, 45]}, "line": [[[0.5718314065678527, 1.2817990647767812], [0.4521037143214604, 1.5380514398084153]], [[1.023935120889313, 2.8198505045851965], [0.0, 0.0], {"subtype": "segment"}], [[2.478001608003481, -0.7934154212845649], [2.2217492329718467, -0.913143113530957]], [[2.384006591183974, -0.7592842505882544], [2.12775421615234, -0.8790119428346466]], [[2.5719966248229875, -0.8275465919808753], [2.3157442497913534, -0.9472742842272674]], [[0.0, 0.0], [4.6997508409753275, -1.7065585348155219], {"subtype": "segment"}], [[5.151854555296788, -0.16850709500710653], [5.271582247543181, -0.42475947003874054]], [[4.6997508409753275, -1.7065585348155219], [5.723685961864641, 1.1132919697696748], {"subtype": "segment"}], [[3.2456843538611597, 1.9067073910542394], [3.501936728892794, 2.0264350833006315]], [[3.3396793706806664, 1.872576220357929], [3.5959317457123006, 1.9923039126043214]], [[3.151689337041653, 1.9408385617505497], [3.407941712073287, 2.060566253996942]], [[5.723685961864641, 1.1132919697696748], [1.023935120889313, 2.8198505045851965], {"subtype": "segment"}], [[1.023935120889313, 2.8198505045851965], [4.6997508409753275, -1.7065585348155219], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.723685961864641, 1.1132919697696748], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
D.

{"path": [[[[3.7066510847030623, 1.503574985250025], [0.0, 0.0], [3.359231874384397, -3.70284191049522], [7.0658829590874594, -2.199266925245195], [3.7066510847030623, 1.503574985250025]]]], "init": {"range": [[-1.0, 8.06588295908746], [-4.70284191049522, 2.503574985250025]], "scale": [45, 45]}, "line": [[[1.7798896723697633, 0.578113290293243], [1.926761412333299, 0.9254616949567821]], [[1.903444708526532, 0.6282324564682438], [2.0503164484900678, 0.9755808611317829]], [[3.7066510847030623, 1.503574985250025], [0.0, 0.0], {"subtype": "segment"}], [[1.867954942706087, -1.8605847185354225], [1.49127693167831, -1.8422571919597974]], [[1.6887797004800111, -1.6630819497337215], [1.670452173904386, -2.0397599607614985]], [[0.0, 0.0], [3.359231874384397, -3.70284191049522], {"subtype": "segment"}], [[5.285993286717696, -2.7773802155384377], [5.1391215467541596, -3.124728620201977]], [[5.162438250560927, -2.8274993817134386], [5.015566510597391, -3.174847786376978]], [[3.359231874384397, -3.70284191049522], [7.0658829590874594, -2.199266925245195], {"subtype": "segment"}], [[5.197928016381373, -0.3386822067097723], [5.574606027409149, -0.3570097332853975]], [[5.377103258607448, -0.5361849755114734], [5.395430785183073, -0.15950696448369645]], [[7.0658829590874594, -2.199266925245195], [3.7066510847030623, 1.503574985250025], {"subtype": "segment"}], [[3.7066510847030623, 1.503574985250025], [3.359231874384397, -3.70284191049522], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [7.0658829590874594, -2.199266925245195], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}

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