Transformations - 4e

Agrandissements & Réductions

Exercice 1 : Calcul du périmètre d'un triangle rectangle et agrandissement ou réduction

Soit un triangle rectangle en \( B \) tel que \( AB=3 cm \) et \( BC=4 cm \).

Calculer le périmètre de ce triangle.
On donnera la réponse suivie de l'unité qui convient.

On multiplie toutes les longueurs de ce triangle par \( 4 \).

Quel est le nouveau périmètre du triangle ?
On donnera la réponse suivie de l'unité qui convient.

Exercice 2 : Reconnaître un agrandissement ou une réduction à l'aide des mesures des diagonales - Losange

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.

{"init": {"range": [[-1.0, 8.3268], [-1.0, 13.6594]], "scale": [45, 45]}, "path": [[[[0.0, 8.450000000000001], [0.0, 0.0], [7.3268, 4.2094000000000005], [7.3268, 12.6594], [0.0, 8.450000000000001]]], [[[3.6634, 6.3297], [3.0528333333333335, 6.683083333333333], [2.69945716669101, 6.072512518790582], [3.3100238333576764, 5.719129185457248], [3.6634, 6.3297]]]], "line": [[[0.28, 3.9450000000000003], [-0.28, 4.505000000000001]], [[0.28, 4.505000000000001], [-0.28, 3.9450000000000003]], [[0.0, 8.450000000000001], [0.0, 0.0], {"subtype": "segment"}], [[3.7666995128761322, 2.486968505947788], [3.560100487123868, 1.7224314940522123]], [[3.5239155034641723, 2.3474840094119602], [3.317316477711908, 1.5829469975163843]], [[4.009483522288092, 2.626453002483616], [3.802884496535828, 1.8619159905880402]], [[0.0, 0.0], [7.3268, 4.2094000000000005], {"subtype": "segment"}], [[7.606800000000001, 8.1544], [7.0468, 8.7144]], [[7.606800000000001, 8.7144], [7.0468, 8.1544]], [[7.3268, 4.2094000000000005], [7.3268, 12.6594], {"subtype": "segment"}], [[3.560100487123868, 10.172431494052212], [3.7666995128761322, 10.936968505947789]], [[3.802884496535828, 10.311915990588039], [4.009483522288092, 11.076453002483616]], [[3.317316477711908, 10.032946997516385], [3.5239155034641723, 10.797484009411962]], [[7.3268, 12.6594], [0.0, 8.450000000000001], {"subtype": "segment"}], [[0.0, 8.450000000000001], [7.3268, 4.2094000000000005], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [7.3268, 12.6594], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.8317, 7.389850000000001], "8,463 cm", "above", {"color": "blue"}], [[1.8317, 3.16485], "14,625 cm", "above", {"color": "red"}]]}
B.

{"init": {"range": [[-1.0, 7.96], [-1.0, 10.325]], "scale": [45, 45]}, "path": [[[[0.0, 7.26], [0.0, 0.0], [6.96, 2.065], [6.96, 9.325], [0.0, 7.26]]], [[[3.48, 4.6625], [2.9, 5.095416666666666], [2.467093520498363, 4.515409063024028], [3.047093520498363, 4.0824923963573605], [3.48, 4.6625]]]], "line": [[[0.24333333333333332, 3.3866666666666667], [-0.24333333333333332, 3.873333333333333]], [[0.0, 7.26], [0.0, 0.0], {"subtype": "segment"}], [[3.6440684192023154, 1.3349959107867004], [3.3159315807976846, 0.7300040892132995]], [[0.0, 0.0], [6.96, 2.065], {"subtype": "segment"}], [[7.203333333333333, 5.451666666666666], [6.716666666666667, 5.938333333333333]], [[6.96, 2.065], [6.96, 9.325], {"subtype": "segment"}], [[3.315931580797684, 7.9900040892133], [3.644068419202316, 8.5949959107867]], [[6.96, 9.325], [0.0, 7.26], {"subtype": "segment"}], [[0.0, 7.26], [6.96, 2.065], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [6.96, 9.325], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.74, 5.96125], "8,685 cm", "above", {"color": "blue"}], [[1.74, 2.33125], "11,636 cm", "above", {"color": "red"}]]}
C.

{"init": {"range": [[-1.0, 7.742], [-1.0, 8.081]], "scale": [45, 45]}, "path": [[[[0.0, 6.75], [0.0, 0.0], [6.742, 0.331], [6.742, 7.081], [0.0, 6.75]]], [[[3.371, 3.5405], [2.8091666666666666, 4.075416666666667], [2.2742399692210586, 3.513592883722088], [2.836073302554392, 2.9786762170554213], [3.371, 3.5405]]]], "line": [[[0.22666666666666666, 3.1483333333333334], [-0.22666666666666666, 3.6016666666666666]], [[0.0, 6.75], [0.0, 0.0], {"subtype": "segment"}], [[3.586279124000468, 0.40300885104590684], [3.155720875999532, -0.07200885104590682]], [[0.0, 0.0], [6.742, 0.331], {"subtype": "segment"}], [[6.968666666666667, 3.479333333333334], [6.515333333333333, 3.932666666666667]], [[6.742, 0.331], [6.742, 7.081], {"subtype": "segment"}], [[3.155720875999532, 6.677991148954093], [3.586279124000468, 7.1530088510459064]], [[6.742, 7.081], [0.0, 6.75], {"subtype": "segment"}], [[0.0, 6.75], [6.742, 0.331], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [6.742, 7.081], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.6855, 5.14525], "9,309 cm", "above", {"color": "blue"}], [[1.6855, 1.77025], "9,777 cm", "above", {"color": "red"}]]}
D.

{"init": {"range": [[-1.0, 7.763200000000001], [-1.0, 12.6856]], "scale": [45, 45]}, "path": [[[[0.0, 7.800000000000001], [0.0, 0.0], [6.763200000000001, 3.8856000000000006], [6.763200000000001, 11.6856], [0.0, 7.800000000000001]]], [[[3.3816000000000006, 5.8428], [2.8180000000000005, 6.1690000000000005], [2.4918066154070866, 5.605396171191307], [3.0554066154070862, 5.279196171191307], [3.3816000000000006, 5.8428]]]], "line": [[[0.26, 3.6400000000000006], [-0.26, 4.16]], [[0.26, 4.16], [-0.26, 3.6400000000000006]], [[0.0, 7.800000000000001], [0.0, 0.0], {"subtype": "segment"}], [[3.4775209762421233, 2.297763612665803], [3.285679023757878, 1.5878363873341974]], [[3.0266363873341975, 2.038720976242123], [3.7365636126658037, 1.8468790237578778]], [[0.0, 0.0], [6.763200000000001, 3.8856000000000006], {"subtype": "segment"}], [[7.023200000000001, 7.525600000000001], [6.503200000000001, 8.0456]], [[7.023200000000001, 8.0456], [6.503200000000001, 7.525600000000001]], [[6.763200000000001, 3.8856000000000006], [6.763200000000001, 11.6856], {"subtype": "segment"}], [[3.285679023757878, 9.387836387334199], [3.4775209762421233, 10.097763612665803]], [[3.7365636126658037, 9.646879023757878], [3.0266363873341975, 9.838720976242124]], [[6.763200000000001, 11.6856], [0.0, 7.800000000000001], {"subtype": "segment"}], [[0.0, 7.800000000000001], [6.763200000000001, 3.8856000000000006], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [6.763200000000001, 11.6856], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.6908000000000003, 6.821400000000001], "7,812 cm", "above", {"color": "blue"}], [[1.6908000000000003, 2.9214], "13,5 cm", "above", {"color": "red"}]]}

Exercice 3 : Reconnaître un agrandissement ou une réduction - Triangle

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.

{"init": {"range": [[-1.0, 9.485735404699051], [-1.4922343358980994, 6.887124622693314]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [8.485735404699051, -0.4922343358980995], [6.131212251820853, 5.887124622693314], [0.0, 0.0]]]]}
B.

{"init": {"range": [[-1.0, 8.986574498540282], [-1.4632793749629172, 6.5408231742995895]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [7.986574498540283, -0.46327937496291716], [5.770552707596096, 5.5408231742995895], [0.0, 0.0]]]]}
C.

{"init": {"range": [[-3.9768758896920535, 1.0], [-1.371765971237477, 3.3921671587679825]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [-1.8103967202002769, 2.3921671587679825], [-2.9768758896920535, -0.371765971237477], [0.0, 0.0]]]], "arc": [[[-1.8103967202002769, 2.3921671587679825], [0.5, 0.5], 247.1185063583199, 307.1185063583199, false], [[0.0, 0.0], [0.5, 0.5], 127.1185063583199, 187.1185063583199, false], [[-2.9768758896920535, -0.371765971237477], [0.5, 0.5], 7.118506358319905, 67.1185063583199, false]], "line": [[[-1.7639259737955921, 2.020057672556476], [-1.7329454761924692, 1.7719846817488047]], [[-0.3454916412506824, 0.14580989618647217], [-0.5758194020844707, 0.24301649364412026]], [[-2.6778549948460557, -0.14546638121244237], [-2.4785077316153905, 0.005400012137580679]]]}
D.

{"init": {"range": [[-1.0, 4.494126343111374], [-1.2026847265462763, 3.4241101387560704]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.494126343111374, -0.20268472654627628], [2.5246168095732924, 2.4241101387560704], [0.0, 0.0]]]]}

Exercice 4 : Reconnaître un agrandissement ou une réduction à l'aide des longueurs - Parallélogramme

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.

{"init": {"range": [[-1.0, 7.235963928537672], [-1.0, 1.9302947898458191]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.6800000000000006, 0.0], [6.235963928537672, 0.9302947898458191], [2.5559639285376714, 0.9302947898458191], [0.0, 0.0]]]], "label": [[[1.8400000000000003, 0.0], "3,68 cm", "below", {}], [[1.2779819642688357, 0.4651473949229096], "2,72 cm", "left", {}], [[0.4464461813655344, 0.07872050720900846], "20\u00b0", "right", {"color": "blue"}], [[5.7895177471721375, 0.8515742826368108], "20\u00b0", "left", {"color": "blue"}], [[3.6012794927909932, 0.4464461813655346], "160\u00b0", "above", {"color": "red"}], [[2.6346844357466814, 0.48384860848028505], "160\u00b0", "below", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.4533333333333334, 0.4533333333333334], 0.0, 20.0, false, {"stroke": "blue"}], [[6.235963928537672, 0.9302947898458191], [0.4533333333333334, 0.4533333333333334], 180.0, 200.0, false, {"stroke": "blue"}], [[3.6800000000000006, 0.0], [0.4533333333333334, 0.4533333333333334], 20.0, 180.0, false, {"stroke": "red"}], [[2.5559639285376714, 0.9302947898458191], [0.4533333333333334, 0.4533333333333334], 200.0, 0.0, false, {"stroke": "red"}]]}
B.

{"init": {"range": [[-1.0, 10.35394589280651], [-1.0, 2.395442184768729]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [5.520000000000001, 0.0], [9.35394589280651, 1.3954421847687288], [3.833945892806507, 1.3954421847687288], [0.0, 0.0]]]], "label": [[[2.7600000000000007, 0.0], "5,52 cm", "below", {}], [[1.9169729464032534, 0.6977210923843644], "4,08 cm", "left", {}], [[0.6696692720483016, 0.11808076081351265], "20\u00b0", "right", {"color": "blue"}], [[8.684276620758208, 1.2773614239552165], "20\u00b0", "left", {"color": "blue"}], [[5.4019192391864905, 0.669669272048302], "160\u00b0", "above", {"color": "red"}], [[3.9520266536200257, 0.7257729127204283], "160\u00b0", "below", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.6800000000000002, 0.6800000000000002], 0.0, 20.0, false, {"stroke": "blue"}], [[9.35394589280651, 1.3954421847687288], [0.6800000000000002, 0.6800000000000002], 180.0, 200.0, false, {"stroke": "blue"}], [[5.520000000000001, 0.0], [0.6800000000000002, 0.6800000000000002], 20.0, 180.0, false, {"stroke": "red"}], [[3.833945892806507, 1.3954421847687288], [0.6800000000000002, 0.6800000000000002], 200.0, 0.0, false, {"stroke": "red"}]]}
C.

{"init": {"range": [[-1.0, 7.235963928537672], [-1.0, 1.9302947898458191]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.6800000000000006, 0.0], [6.235963928537672, 0.9302947898458191], [2.5559639285376714, 0.9302947898458191], [0.0, 0.0]]]], "label": [[[1.8400000000000003, 0.0], "3,68 cm", "below", {}], [[1.2779819642688357, 0.4651473949229096], "2,72 cm", "left", {}], [[0.4464461813655344, 0.07872050720900846], "20\u00b0", "right", {"color": "blue"}], [[5.7895177471721375, 0.8515742826368108], "20\u00b0", "left", {"color": "blue"}], [[3.6012794927909932, 0.4464461813655346], "160\u00b0", "above", {"color": "red"}], [[2.6346844357466814, 0.48384860848028505], "160\u00b0", "below", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.4533333333333334, 0.4533333333333334], 0.0, 20.0, false, {"stroke": "blue"}], [[6.235963928537672, 0.9302947898458191], [0.4533333333333334, 0.4533333333333334], 180.0, 200.0, false, {"stroke": "blue"}], [[3.6800000000000006, 0.0], [0.4533333333333334, 0.4533333333333334], 20.0, 180.0, false, {"stroke": "red"}], [[2.5559639285376714, 0.9302947898458191], [0.4533333333333334, 0.4533333333333334], 200.0, 0.0, false, {"stroke": "red"}]]}
D.

{"init": {"range": [[-1.0, 7.8749549106720895], [-1.0, 2.162868487307274]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.6800000000000006, 0.0], [6.8749549106720895, 1.1628684873072739], [3.194954910672089, 1.1628684873072739], [0.0, 0.0]]]], "label": [[[1.8400000000000003, 0.0], "3,68 cm", "below", {}], [[1.5974774553360445, 0.5814342436536369], "3,4 cm", "left", {}], [[0.558057726706918, 0.09840063401126056], "20\u00b0", "right", {"color": "blue"}], [[6.316897183965171, 1.0644678532960135], "20\u00b0", "left", {"color": "blue"}], [[3.5815993659887413, 0.5580577267069182], "160\u00b0", "above", {"color": "red"}], [[3.2933555446833456, 0.6048107606003553], "160\u00b0", "below", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.5666666666666668, 0.5666666666666668], 0.0, 20.0, false, {"stroke": "blue"}], [[6.8749549106720895, 1.1628684873072739], [0.5666666666666668, 0.5666666666666668], 180.0, 200.0, false, {"stroke": "blue"}], [[3.6800000000000006, 0.0], [0.5666666666666668, 0.5666666666666668], 20.0, 180.0, false, {"stroke": "red"}], [[3.194954910672089, 1.1628684873072739], [0.5666666666666668, 0.5666666666666668], 200.0, 0.0, false, {"stroke": "red"}]]}

Exercice 5 : Reconnaître un agrandissement ou une réduction à l'aide des longeurs - Triangle

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.

{"init": {"range": [[-1.0, 5.59], [-1.0, 5.219263955852537]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [4.59, 0.0], [3.207461873638344, 4.219263955852537], [0.0, 0.0]]]], "label": [[[2.295, 0.0], "4,59 cm", "below", {}], [[3.898730936819172, 2.1096319779262687], "4,44 cm", "above right", {}], [[1.603730936819172, 2.1096319779262687], "5,3 cm", "above left", {}]]}
B.

{"init": {"range": [[-1.0, 7.8999999999999995], [-1.0, 6.712940877205551]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [6.8999999999999995, 0.0], [3.3048913043478256, 5.712940877205551], [0.0, 0.0]]]], "label": [[[3.4499999999999997, 0.0], "6,9 cm", "below", {}], [[5.1024456521739125, 2.8564704386027757], "6,75 cm", "above right", {}], [[1.6524456521739128, 2.8564704386027757], "6,6 cm", "above left", {}]]}
C.

{"init": {"range": [[-1.0, 3.76], [-1.0, 3.2851763508822205]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [2.76, 0.0], [1.32195652173913, 2.2851763508822205], [0.0, 0.0]]]], "label": [[[1.38, 0.0], "2,76 cm", "below", {}], [[2.040978260869565, 1.1425881754411102], "2,7 cm", "above right", {}], [[0.660978260869565, 1.1425881754411102], "2,64 cm", "above left", {}]]}
D.

{"init": {"range": [[-1.0, 4.38], [-1.0, 6.117844392016587]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.38, 0.0], [1.626213017751479, 5.117844392016587], [0.0, 0.0]]]], "label": [[[1.69, 0.0], "3,38 cm", "below", {}], [[2.5031065088757396, 2.5589221960082935], "5,41 cm", "above right", {}], [[0.8131065088757395, 2.5589221960082935], "5,37 cm", "above left", {}]]}

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