Agrandissement / Réduction

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

Exemple d'exercice parmi les 119 exercices du chapitre

On considère la figure modèle suivante :

{"path": [[[[0.0, 6.2], [0.0, 0.0], [5.884, 1.955], [5.884, 8.155000000000001], [0.0, 6.2]]], [[[2.942, 4.077500000000001], [2.4516666666666667, 4.43125], [2.0978932732521, 3.940933544647215], [2.5882266065854336, 3.587183544647215], [2.942, 4.077500000000001]]]], "init": {"range": [[-1.0, 6.884], [-1.0, 9.155000000000001]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.0333333333333334, 1.0333333333333334], 18.379426842507087, 90.0, false], [[5.884, 8.155000000000001], [1.0333333333333334, 1.0333333333333334], 198.3794268425071, 270.0, false], [[5.884, 1.955], [1.0333333333333334, 1.0333333333333334], 90.0, 198.3794268425071, false], [[5.884, 1.955], [0.8266666666666668, 0.8266666666666668], 90.0, 198.3794268425071, false], [[0.0, 6.2], [1.0333333333333334, 1.0333333333333334], 270.0, 18.379426842507087, false], [[0.0, 6.2], [0.8266666666666668, 0.8266666666666668], 270.0, 18.379426842507087, false]], "line": [[[0.20666666666666667, 2.8933333333333335], [-0.20666666666666667, 3.3066666666666666]], [[0.20666666666666667, 3.1], [-0.20666666666666667, 3.513333333333333]], [[0.20666666666666667, 2.686666666666667], [-0.20666666666666667, 3.1]], [[0.0, 6.2], [0.0, 0.0], {"subtype": "segment"}], [[3.072960737114043, 1.2387881695690965], [2.8110392628859575, 0.7162118304309036]], [[2.8768362837724735, 1.1736244533415694], [2.614914809544388, 0.6510481142033767]], [[3.269085190455612, 1.3039518857966232], [3.007163716227527, 0.7813755466584306]], [[0.0, 0.0], [5.884, 1.955], {"subtype": "segment"}], [[6.090666666666667, 4.848333333333334], [5.677333333333333, 5.261666666666668]], [[6.090666666666667, 5.055000000000001], [5.677333333333333, 5.468333333333335]], [[6.090666666666667, 4.641666666666667], [5.677333333333333, 5.055000000000001]], [[5.884, 1.955], [5.884, 8.155000000000001], {"subtype": "segment"}], [[2.8110392628859575, 6.916211830430904], [3.072960737114043, 7.438788169569096]], [[3.007163716227527, 6.981375546658431], [3.269085190455612, 7.503951885796623]], [[2.614914809544388, 6.851048114203377], [2.8768362837724735, 7.373624453341569]], [[5.884, 8.155000000000001], [0.0, 6.2], {"subtype": "segment"}], [[0.0, 6.2], [5.884, 1.955], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.884, 8.155000000000001], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.604606722286847, 0.8379907452611477], "72\u00b0", "above right"], [[5.279393277713153, 7.317009254738854], "72\u00b0", "below left"], [[5.046009254738853, 2.5596067222868473], "108\u00b0", "above left"], [[0.8379907452611481, 5.595393277713154], "108\u00b0", "below right"]]}

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

A.

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B.

{"path": [[[[0.0, 4.23], [0.0, 0.0], [4.053, 1.211], [4.053, 5.441000000000001], [0.0, 4.23]]], [[[2.0265, 2.7205000000000004], [1.68875, 2.972083333333334], [1.4371624310678528, 2.6343364883888944], [1.7749124310678528, 2.382753155055561], [2.0265, 2.7205000000000004]]]], "init": {"range": [[-1.0, 5.053], [-1.0, 6.441000000000001]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.7050000000000001, 0.7050000000000001], 16.635673098787947, 90.0, false], [[4.053, 5.441000000000001], [0.7050000000000001, 0.7050000000000001], 196.63567309878795, 270.0, false], [[4.053, 1.211], [0.7050000000000001, 0.7050000000000001], 90.0, 196.63567309878795, false], [[4.053, 1.211], [0.5640000000000001, 0.5640000000000001], 90.0, 196.63567309878795, false], [[0.0, 4.23], [0.7050000000000001, 0.7050000000000001], 270.0, 16.635673098787947, false], [[0.0, 4.23], [0.5640000000000001, 0.5640000000000001], 270.0, 16.635673098787947, false]], "line": [[[0.14, 1.975], [-0.14, 2.2550000000000003]], [[0.14, 2.115], [-0.14, 2.3950000000000005]], [[0.0, 4.23], [0.0, 0.0], {"subtype": "segment"}], [[2.12056033550455, 0.7797201288163096], [1.9324396644954498, 0.43127987118369054]], [[1.9864201033441202, 0.7396402321604298], [1.7982994323350203, 0.3911999745278108]], [[0.0, 0.0], [4.053, 1.211], {"subtype": "segment"}], [[4.193, 3.1860000000000004], [3.913, 3.4660000000000006]], [[4.193, 3.3260000000000005], [3.913, 3.6060000000000008]], [[4.053, 1.211], [4.053, 5.441000000000001], {"subtype": "segment"}], [[1.9324396644954498, 4.661279871183691], [2.12056033550455, 5.00972012881631]], [[2.0665798966558797, 4.701359767839571], [2.25470056766498, 5.04980002547219]], [[4.053, 5.441000000000001], [0.0, 4.23], {"subtype": "segment"}], [[0.0, 4.23], [4.053, 1.211], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [4.053, 5.441000000000001], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.4211497416283335, 0.5653829632438424], "73\u00b0", "above right"], [[3.6318502583716668, 4.875617036756158], "73\u00b0", "below left"], [[3.487617036756158, 1.632149741628334], "107\u00b0", "above left"], [[0.5653829632438424, 3.8088502583716672], "107\u00b0", "below right"]]}
C.

{"path": [[[[0.0, 6.25], [0.0, 0.0], [5.511, 2.949], [5.511, 9.199], [0.0, 6.25]]], [[[2.7555, 4.5995], [2.29625, 4.874583333333334], [2.0211318541237975, 4.415354187277229], [2.4803818541237974, 4.140270853943896], [2.7555, 4.5995]]]], "init": {"range": [[-1.0, 6.511], [-1.0, 10.199]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.0416666666666667, 1.0416666666666667], 28.151752059234582, 90.0, false], [[5.511, 9.199], [1.0416666666666667, 1.0416666666666667], 208.1517520592347, 270.0, false], [[5.511, 2.949], [1.0416666666666667, 1.0416666666666667], 90.0, 208.1517520592347, false], [[5.511, 2.949], [0.8333333333333335, 0.8333333333333335], 90.0, 208.1517520592347, false], [[0.0, 6.25], [1.0416666666666667, 1.0416666666666667], 270.0, 28.151752059234582, false], [[0.0, 6.25], [0.8333333333333335, 0.8333333333333335], 270.0, 28.151752059234582, false]], "line": [[[0.21, 2.915], [-0.21, 3.335]], [[0.21, 3.125], [-0.21, 3.545]], [[0.21, 2.705], [-0.21, 3.125]], [[0.0, 6.25], [0.0, 0.0], {"subtype": "segment"}], [[2.8415774466380186, 1.7587370017789363], [2.6694225533619815, 1.1902629982210635]], [[2.6564202224295412, 1.6596572242084773], [2.484265329153504, 1.0911832206506045]], [[3.026734670846496, 1.8578167793493954], [2.854579777570459, 1.2893427757915226]], [[0.0, 0.0], [5.511, 2.949], {"subtype": "segment"}], [[5.721, 5.864], [5.301, 6.284]], [[5.721, 6.074], [5.301, 6.494]], [[5.721, 5.654], [5.301, 6.074]], [[5.511, 2.949], [5.511, 9.199], {"subtype": "segment"}], [[2.6694225533619815, 7.440262998221064], [2.8415774466380186, 8.008737001778936]], [[2.854579777570459, 7.539342775791523], [3.026734670846496, 8.107816779349395]], [[2.484265329153504, 7.3411832206506045], [2.6564202224295412, 7.909657224208477]], [[5.511, 9.199], [0.0, 6.25], {"subtype": "segment"}], [[0.0, 6.25], [5.511, 2.949], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.511, 9.199], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.5353150921904296, 0.8935922988240199], "62\u00b0", "above right"], [[4.975684907809571, 8.30540770117598], "62\u00b0", "below left"], [[4.61740770117598, 3.48431509219043], "118\u00b0", "above left"], [[0.8935922988240191, 5.71468490780957], "118\u00b0", "below right"]]}
D.

{"path": [[[[0.0, 4.340000000000001], [0.0, 0.0], [4.1188, 1.3685000000000003], [4.1188, 5.708500000000002], [0.0, 4.340000000000001]]], [[[2.0594, 2.854250000000001], [1.7161666666666668, 3.1018750000000006], [1.4685252912764701, 2.758653481253051], [1.8117586246098036, 2.511028481253051], [2.0594, 2.854250000000001]]]], "init": {"range": [[-1.0, 5.1188], [-1.0, 6.708500000000002]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.7233333333333335, 0.7233333333333335], 18.379426842507087, 90.0, false], [[4.1188, 5.708500000000002], [0.7233333333333336, 0.7233333333333336], 198.3794268425071, 270.0, false], [[4.1188, 1.3685000000000003], [0.7233333333333336, 0.7233333333333336], 90.0, 198.3794268425071, false], [[4.1188, 1.3685000000000003], [0.5786666666666669, 0.5786666666666669], 90.0, 198.3794268425071, false], [[0.0, 4.340000000000001], [0.7233333333333335, 0.7233333333333335], 270.0, 18.379426842507087, false], [[0.0, 4.340000000000001], [0.5786666666666668, 0.5786666666666668], 270.0, 18.379426842507087, false]], "line": [[[0.1433333333333333, 2.0266666666666673], [-0.1433333333333333, 2.3133333333333335]], [[0.0, 4.340000000000001], [0.0, 0.0], {"subtype": "segment"}], [[2.150227607998449, 0.8654659885721154], [1.9685723920015512, 0.5030340114278848]], [[0.0, 0.0], [4.1188, 1.3685000000000003], {"subtype": "segment"}], [[4.262133333333334, 3.3951666666666673], [3.9754666666666667, 3.6818333333333344]], [[4.1188, 1.3685000000000003], [4.1188, 5.708500000000002], {"subtype": "segment"}], [[1.9685723920015512, 4.843034011427886], [2.150227607998449, 5.205465988572117]], [[4.1188, 5.708500000000002], [0.0, 4.340000000000001], {"subtype": "segment"}], [[0.0, 4.340000000000001], [4.1188, 1.3685000000000003], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [4.1188, 5.708500000000002], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.4232247056007929, 0.5865935216828033], "72\u00b0", "above right"], [[3.695575294399207, 5.121906478317198], "72\u00b0", "below left"], [[3.532206478317197, 1.7917247056007932], "108\u00b0", "above left"], [[0.5865935216828032, 3.9167752943992076], "108\u00b0", "below right"]]}

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