Pour aller plus loin (Ancien programme) - 5e
Proportionnalité
Exercice 1 : Reconnaître un agrandissement ou une réduction - Cercles et Ellipses
On considère la figure modèle suivante :
{"init": {"range": [[-4.0, 4.0], [-4.0, 4.0]], "scale": [20, 20]}, "circle": [[[0.0, 0.0], 3.0, {}]]}
Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.
- A.
{"init": {"range": [[-6.0, 6.0], [-6.0, 6.0]], "scale": [20, 20]}, "circle": [[[0.0, 0.0], 5.0, {}]]}
- B.
{"init": {"range": [[-4.0, 4.0], [-4.0, 4.0]], "scale": [20, 20]}, "circle": [[[0.0, 0.0], 3.0, {}]]}
- C.
{"init": {"range": [[-4.0, 4.0], [-8.0, 8.0]], "scale": [20, 20]}, "ellipse": [[[0.0, 0.0], [3.0, 7.0], {}]]}
- D.
{"init": {"range": [[-8.0, 8.0], [-4.0, 4.0]], "scale": [20, 20]}, "ellipse": [[[0.0, 0.0], [7.0, 3.0], {}]]}
Exercice 2 : Reconnaître un agrandissement ou une réduction - Quadrilatères
On considère la figure modèle suivante :
{"path": [[[[1.5384371893542197, 3.6923178376748513], [0.0, 0.0], [3.9092363668963945, -0.8488203742457404], [5.447673556250614, 2.843497463429111], [1.5384371893542197, 3.6923178376748513]]], [[[2.7238367781253072, 1.4217487317145554], [2.526270179996793, 1.8001769160412713], [2.147825522642713, 1.6026418743169175], [2.3453921207712276, 1.2242136899902016], [2.7238367781253072, 1.4217487317145554]]]], "init": {"range": [[-1.0, 6.447673556250614], [-1.8488203742457405, 4.692317837674851]], "scale": [45, 45]}, "line": [[[0.8410146162877976, 1.6718004179364567], [0.6974225730664221, 2.0205174197383946]], [[0.8922958559329383, 1.7948776791922851], [0.7487038127115627, 2.143594680994223]], [[1.5384371893542197, 3.6923178376748513], [0.0, 0.0], {"subtype": "segment"}], [[2.1132070661088598, -0.32240468799660615], [1.796029300787535, -0.5264156862491343]], [[1.9829098752153964, -0.29411299622940706], [1.6657321098940718, -0.4981239944819352]], [[0.0, 0.0], [3.9092363668963945, -0.8488203742457404], {"subtype": "segment"}], [[4.606658939962816, 1.171697045492654], [4.750250983184191, 0.8229800436907161]], [[4.555377700317676, 1.0486197842368257], [4.698969743539051, 0.6999027824348877]], [[3.9092363668963945, -0.8488203742457404], [5.447673556250614, 2.843497463429111], {"subtype": "segment"}], [[3.3344664901417542, 3.1659021514257173], [3.651644255463079, 3.3699131496782453]], [[3.4647636810352176, 3.1376104596585184], [3.781941446356542, 3.3416214579110464]], [[5.447673556250614, 2.843497463429111], [1.5384371893542197, 3.6923178376748513], {"subtype": "segment"}], [[1.5384371893542197, 3.6923178376748513], [3.9092363668963945, -0.8488203742457404], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.447673556250614, 2.843497463429111], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.
- A.
{"path": [[[[2.4614995029667517, 5.907708540279763], [0.0, 0.0], [6.254778187034232, -1.3581125987931848], [8.716277690000982, 4.549595941486578], [2.4614995029667517, 5.907708540279763]]], [[[4.358138845000491, 2.274797970743289], [4.042032287994868, 2.8802830656660348], [3.4365208362283406, 2.5642269989070683], [3.752627393233964, 1.9587419039843226], [4.358138845000491, 2.274797970743289]]]], "init": {"range": [[-1.0, 9.716277690000982], [-2.358112598793185, 6.907708540279763]], "scale": [45, 45]}, "line": [[[1.3456233860604763, 2.674880668698331], [1.1158761169062754, 3.232827871581432]], [[1.4276733694927013, 2.8718042867076563], [1.1979261003385004, 3.4297514895907573]], [[2.4614995029667517, 5.907708540279763], [0.0, 0.0], {"subtype": "segment"}], [[3.3811313057741756, -0.51584750079457], [2.873646881260056, -0.8422650979986148]], [[3.172655800344635, -0.4705807939670514], [2.665171375830515, -0.7969983911710963]], [[0.0, 0.0], [6.254778187034232, -1.3581125987931848], {"subtype": "segment"}], [[7.370654303940507, 1.8747152727882468], [7.600401573094707, 1.3167680699051458]], [[7.2886043205082816, 1.6777916547789213], [7.518351589662482, 1.1198444518958204]], [[6.254778187034232, -1.3581125987931848], [8.716277690000982, 4.549595941486578], {"subtype": "segment"}], [[5.335146384226808, 5.065443442281147], [5.842630808740927, 5.3918610394851925]], [[5.5436218896563485, 5.020176735453628], [6.051106314170468, 5.3465943326576735]], [[8.716277690000982, 4.549595941486578], [2.4614995029667517, 5.907708540279763], {"subtype": "segment"}], [[2.4614995029667517, 5.907708540279763], [6.254778187034232, -1.3581125987931848], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [8.716277690000982, 4.549595941486578], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
- B.
{"path": [[[[2.6153432219021737, 6.276940324047248], [0.0, 0.0], [6.645701823723871, -1.4429946362177588], [9.261045045626044, 4.833945687829489], [2.6153432219021737, 6.276940324047248]]], [[[4.630522522813022, 2.4169728439147447], [4.294659305994547, 3.060300757270162], [3.6513033884926123, 2.7244911863387604], [3.987166605311087, 2.081163272983343], [4.630522522813022, 2.4169728439147447]]]], "init": {"range": [[-1.0, 10.261045045626044], [-2.442994636217759, 7.276940324047248]], "scale": [45, 45]}, "line": [[[1.429724847689256, 2.842060710491977], [1.1856183742129178, 3.4348796135552715]], [[1.516902955085995, 3.051292054626885], [1.2727964816096569, 3.6441109576901796]], [[2.6153432219021737, 6.276940324047248], [0.0, 0.0], {"subtype": "segment"}], [[3.5924520123850616, -0.5480879695942306], [3.0532498113388096, -0.8949066666235282]], [[3.370946787866174, -0.4999920935899921], [2.831744586819923, -0.8468107906192898]], [[0.0, 0.0], [6.645701823723871, -1.4429946362177588], {"subtype": "segment"}], [[7.8313201979367895, 1.9918849773375125], [8.075426671413128, 1.3990660742742178]], [[7.74414209054005, 1.7826536332026042], [7.988248564016388, 1.1898347301393095]], [[6.645701823723871, -1.4429946362177588], [9.261045045626044, 4.833945687829489], {"subtype": "segment"}], [[5.668593033240984, 5.38203365742372], [6.207795234287235, 5.728852354453017]], [[5.890098257759871, 5.333937781419481], [6.429300458806122, 5.680756478448778]], [[9.261045045626044, 4.833945687829489], [2.6153432219021737, 6.276940324047248], {"subtype": "segment"}], [[2.6153432219021737, 6.276940324047248], [6.645701823723871, -1.4429946362177588], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [9.261045045626044, 4.833945687829489], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
- C.
{"path": [[[[2.1968308532452974, -2.043020852127931], [0.0, 0.0], [-2.043020852127931, -2.1968308532452974], [0.15381000111736615, -4.239851705373229], [2.1968308532452974, -2.043020852127931]]], [[[0.0, 0.0], [0.3661384755408829, -0.3405034753546552], [0.02563500018622772, -0.7066419508955382], [-0.3405034753546552, -0.3661384755408829], [0.0, 0.0]]], [[[0.0769050005586831, -2.119925852686614], [0.4302259760064521, -2.1071083525935004], [0.4174084759133383, -1.7537873771457313], [0.06408750046556926, -1.766604877238845], [0.0769050005586831, -2.119925852686614]]]], "init": {"range": [[-3.043020852127931, 3.1968308532452974], [-5.239851705373229, 1.0]], "scale": [45, 45]}, "line": [[[0.9570870364435411, -1.0266374261012112], [1.2397438168017563, -1.01638342602672]], [[2.1968308532452974, -2.043020852127931], [0.0, 0.0], {"subtype": "segment"}], [[-1.01638342602672, -1.2397438168017563], [-1.0266374261012112, -0.9570870364435411]], [[0.0, 0.0], [-2.043020852127931, -2.1968308532452974], {"subtype": "segment"}], [[-0.8032770353261749, -3.2132142792720177], [-1.08593381568439, -3.223468279346509]], [[-2.043020852127931, -2.1968308532452974], [0.15381000111736615, -4.239851705373229], {"subtype": "segment"}], [[1.1701934271440861, -3.0001078885714723], [1.1804474272185774, -3.282764668929688]], [[0.15381000111736615, -4.239851705373229], [2.1968308532452974, -2.043020852127931], {"subtype": "segment"}], [[2.1968308532452974, -2.043020852127931], [-2.043020852127931, -2.1968308532452974], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [0.15381000111736615, -4.239851705373229], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
- D.
{"path": [[[[3.7227339296996687, 1.4633017763478802], [0.0, 0.0], [1.09747633226091, -2.7920504472747516], [4.820210261960579, -1.3287486709268717], [3.7227339296996687, 1.4633017763478802]]], [[[0.0, 0.0], [0.4653417412124586, 0.18291272204348502], [0.6482544632559436, -0.28242901916897356], [0.182912722043485, -0.4653417412124586], [0.0, 0.0]]]], "init": {"range": [[-1.0, 5.820210261960579], [-3.7920504472747516, 2.46330177634788]], "scale": [45, 45]}, "line": [[[1.8048811610160396, 0.6019999955227513], [1.917852768683629, 0.8613017808251289]], [[1.8979495092585312, 0.6385825399314484], [2.0109211169261205, 0.8978843252338258]], [[3.7227339296996687, 1.4633017763478802], [0.0, 0.0], {"subtype": "segment"}], [[0.6783890587816437, -1.4525110274711706], [0.4190872734792663, -1.339539419803581]], [[0.6418065143729468, -1.359442679228679], [0.38250472907056926, -1.2464710715610894]], [[0.7149716031903408, -1.5455793757136622], [0.4556698178879633, -1.4326077680460727]], [[0.0, 0.0], [1.09747633226091, -2.7920504472747516], {"subtype": "segment"}], [[3.015329100944539, -1.930748666449623], [2.90235749327695, -2.1900504517520005]], [[2.922260752702047, -1.9673312108583199], [2.809289145034458, -2.2266329961606974]], [[1.09747633226091, -2.7920504472747516], [4.820210261960579, -1.3287486709268717], {"subtype": "segment"}], [[4.141821203178935, 0.12376235654429896], [4.401122988481312, 0.010790748876709548]], [[4.178403747587632, 0.030694008301807248], [4.437705532890009, -0.08227759936578216]], [[4.105238658770238, 0.21683070478679067], [4.364540444072615, 0.10385909711920127]], [[4.820210261960579, -1.3287486709268717], [3.7227339296996687, 1.4633017763478802], {"subtype": "segment"}], [[3.7227339296996687, 1.4633017763478802], [1.09747633226091, -2.7920504472747516], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [4.820210261960579, -1.3287486709268717], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
Exercice 3 : Comparer des proportions - Problème contextualisé
Dans la classe de 4ème A, 15 élèves sur 32 sont nés entre Mars et Novembre.
Dans la classe de 4ème C, 8 élèves sur 21 sont nés entre Mars et Novembre.
Dans quelle classe la proportion d'élèves nés entre Mars et Novembre est-elle la plus grande ?
Dans la classe de 4ème C, 8 élèves sur 21 sont nés entre Mars et Novembre.
Dans quelle classe la proportion d'élèves nés entre Mars et Novembre est-elle la plus grande ?
Exercice 4 : Reconnaître un agrandissement ou une réduction à l'aide des longueurs - Parallélogramme
On considère la figure modèle suivante :
{"init": {"range": [[-2.774996699310938, 4.1], [-1.0, 4.80649270555393]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.1, 0.0], [1.3250033006890625, 3.80649270555393], [-1.7749966993109376, 3.80649270555393], [0.0, 0.0]]]], "label": [[[1.55, 0.0], "3,1 cm", "below", {}], [[-0.8874983496554688, 1.903246352776965], "4,2 cm", "left", {}], [[0.27760479764585905, 0.4357522470033243], "115\u00b0", "above right", {"color": "blue"}], [[1.0473985030432036, 3.3707404585506056], "115\u00b0", "below left", {"color": "blue"}], [[2.6642477529966757, 0.27760479764585905], "65\u00b0", "above left", {"color": "red"}], [[-1.3392444523076132, 3.528887907908071], "65\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.5166666666666667, 0.5166666666666667], 0.0, 115.0, false, {"stroke": "blue"}], [[1.3250033006890625, 3.80649270555393], [0.5166666666666667, 0.5166666666666667], 180.0, 295.0, false, {"stroke": "blue"}], [[3.1, 0.0], [0.5166666666666667, 0.5166666666666667], 115.0, 180.0, false, {"stroke": "red"}], [[-1.7749966993109376, 3.80649270555393], [0.5166666666666667, 0.5166666666666667], 295.0, 0.0, false, {"stroke": "red"}]]}
Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.
- A.
{"init": {"range": [[-3.6624950489664068, 5.65], [-1.0, 6.709739058330896]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [4.65, 0.0], [1.9875049510335936, 5.709739058330896], [-2.6624950489664068, 5.709739058330896], [0.0, 0.0]]]], "label": [[[2.325, 0.0], "4,65 cm", "below", {}], [[-1.3312475244832034, 2.854869529165448], "6,3 cm", "left", {}], [[0.41640719646878843, 0.6536283705049865], "115\u00b0", "above right", {"color": "blue"}], [[1.5710977545648055, 5.056110687825909], "115\u00b0", "below left", {"color": "blue"}], [[3.9963716294950133, 0.4164071964687878], "65\u00b0", "above left", {"color": "red"}], [[-2.0088666784614206, 5.293331861862107], "65\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.775, 0.775], 0.0, 115.0, false, {"stroke": "blue"}], [[1.9875049510335936, 5.709739058330896], [0.775, 0.775], 180.0, 295.0, false, {"stroke": "blue"}], [[4.65, 0.0], [0.775, 0.775], 115.0, 180.0, false, {"stroke": "red"}], [[-2.6624950489664068, 5.709739058330896], [0.775, 0.775], 295.0, 0.0, false, {"stroke": "red"}]]}
- B.
{"init": {"range": [[-1.2928432956321316, 3.4800000000000004], [-1.0, 4.347214185588266]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [2.4800000000000004, 0.0], [2.187156704367869, 3.3472141855882653], [-0.2928432956321315, 3.3472141855882653], [0.0, 0.0]]]], "label": [[[1.2400000000000002, 0.0], "2,48 cm", "below", {}], [[-0.14642164781606576, 1.6736070927941327], "3,36 cm", "left", {}], [[0.27924395248113953, 0.30474129921485127], "95\u00b0", "above right", {"color": "blue"}], [[1.9079127518867287, 3.0424728863734143], "95\u00b0", "below left", {"color": "blue"}], [[2.175258700785149, 0.2792439524811394], "85\u00b0", "above left", {"color": "red"}], [[0.011898003582720196, 3.0679702331071264], "85\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.4133333333333334, 0.4133333333333334], 0.0, 95.0, false, {"stroke": "blue"}], [[2.187156704367869, 3.3472141855882653], [0.4133333333333334, 0.4133333333333334], 180.0, 275.0, false, {"stroke": "blue"}], [[2.4800000000000004, 0.0], [0.4133333333333334, 0.4133333333333334], 95.0, 180.0, false, {"stroke": "red"}], [[-0.2928432956321315, 3.3472141855882653], [0.4133333333333334, 0.4133333333333334], 275.0, 0.0, false, {"stroke": "red"}]]}
- C.
{"init": {"range": [[-4.194994058759688, 6.58], [-1.0, 7.851686869997074]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [5.58, 0.0], [2.385005941240312, 6.851686869997074], [-3.194994058759688, 6.851686869997074], [0.0, 0.0]]]], "label": [[[2.79, 0.0], "5,58 cm", "below", {}], [[-1.597497029379844, 3.425843434998537], "7,56 cm", "left", {}], [[0.49968863576254613, 0.7843540446059838], "115\u00b0", "above right", {"color": "blue"}], [[1.8853173054777663, 6.06733282539109], "115\u00b0", "below left", {"color": "blue"}], [[4.795645955394017, 0.49968863576254635], "65\u00b0", "above left", {"color": "red"}], [[-2.4106400141537048, 6.351998234234528], "65\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.93, 0.93], 0.0, 115.0, false, {"stroke": "blue"}], [[2.385005941240312, 6.851686869997074], [0.93, 0.93], 180.0, 295.0, false, {"stroke": "blue"}], [[5.58, 0.0], [0.93, 0.93], 115.0, 180.0, false, {"stroke": "red"}], [[-3.194994058759688, 6.851686869997074], [0.93, 0.93], 295.0, 0.0, false, {"stroke": "red"}]]}
- D.
{"init": {"range": [[-3.6624950489664068, 5.65], [-1.0, 6.709739058330896]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [4.65, 0.0], [1.9875049510335936, 5.709739058330896], [-2.6624950489664068, 5.709739058330896], [0.0, 0.0]]]], "label": [[[2.325, 0.0], "4,65 cm", "below", {}], [[-1.3312475244832034, 2.854869529165448], "6,3 cm", "left", {}], [[0.41640719646878843, 0.6536283705049865], "115\u00b0", "above right", {"color": "blue"}], [[1.5710977545648055, 5.056110687825909], "115\u00b0", "below left", {"color": "blue"}], [[3.9963716294950133, 0.4164071964687878], "65\u00b0", "above left", {"color": "red"}], [[-2.0088666784614206, 5.293331861862107], "65\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.775, 0.775], 0.0, 115.0, false, {"stroke": "blue"}], [[1.9875049510335936, 5.709739058330896], [0.775, 0.775], 180.0, 295.0, false, {"stroke": "blue"}], [[4.65, 0.0], [0.775, 0.775], 115.0, 180.0, false, {"stroke": "red"}], [[-2.6624950489664068, 5.709739058330896], [0.775, 0.775], 295.0, 0.0, false, {"stroke": "red"}]]}
Exercice 5 : Reconnaître un agrandissement ou une réduction à l'aide des mesures des diagonales - Losange
On considère la figure modèle suivante :
{"init": {"range": [[-1.0, 6.417], [-1.0, 9.239]], "scale": [45, 45]}, "path": [[[[0.0, 5.9], [0.0, 0.0], [5.417, 2.339], [5.417, 8.239], [0.0, 5.9]]], [[[2.7085, 4.1195], [2.257083333333333, 4.416250000000001], [1.9602993652470497, 3.9648556649320863], [2.4117160319137163, 3.6681056649320865], [2.7085, 4.1195]]]], "line": [[[0.19666666666666668, 2.7533333333333334], [-0.19666666666666668, 3.146666666666667]], [[0.0, 5.9], [0.0, 0.0], {"subtype": "segment"}], [[2.811092912168028, 1.4280154732862984], [2.6059070878319717, 0.9109845267137016]], [[0.0, 0.0], [5.417, 2.339], {"subtype": "segment"}], [[5.613666666666666, 5.092333333333334], [5.2203333333333335, 5.485666666666667]], [[5.417, 2.339], [5.417, 8.239], {"subtype": "segment"}], [[2.6059070878319717, 6.810984526713702], [2.811092912168028, 7.328015473286299]], [[5.417, 8.239], [0.0, 5.9], {"subtype": "segment"}], [[0.0, 5.9], [5.417, 2.339], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [5.417, 8.239], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.35425, 5.00975], "6,48 cm", "above", {"color": "blue"}], [[1.35425, 2.05975], "9,86 cm", "above", {"color": "red"}]]}
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.
{"init": {"range": [[-1.0, 6.9587], [-1.0, 10.0629]], "scale": [45, 45]}, "path": [[[[0.0, 6.490000000000001], [0.0, 0.0], [5.9587, 2.5729], [5.9587, 9.0629], [0.0, 6.490000000000001]]], [[[2.97935, 4.53145], [2.482791666666667, 4.857875000000001], [2.1563293017717546, 4.361341231425295], [2.6528876351050883, 4.034916231425295], [2.97935, 4.53145]]]], "line": [[[0.21666666666666667, 3.0283333333333338], [-0.21666666666666667, 3.4616666666666673]], [[0.21666666666666667, 3.2450000000000006], [-0.21666666666666667, 3.678333333333334]], [[0.0, 6.490000000000001], [0.0, 0.0], {"subtype": "segment"}], [[3.0923760896766415, 1.5712551824340575], [2.866323910323359, 1.0016448175659427]], [[2.8934604536212922, 1.4853656360553493], [2.6674082742680096, 0.9157552711872345]], [[0.0, 0.0], [5.9587, 2.5729], {"subtype": "segment"}], [[6.175366666666667, 5.601233333333334], [5.7420333333333335, 6.0345666666666675]], [[6.175366666666667, 5.817900000000001], [5.7420333333333335, 6.251233333333334]], [[5.9587, 2.5729], [5.9587, 9.0629], {"subtype": "segment"}], [[2.866323910323359, 7.491644817565943], [3.0923760896766415, 8.061255182434058]], [[3.065239546378708, 7.577534363944651], [3.2912917257319907, 8.147144728812766]], [[5.9587, 9.0629], [0.0, 6.490000000000001], {"subtype": "segment"}], [[0.0, 6.490000000000001], [5.9587, 2.5729], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [5.9587, 9.0629], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.489675, 5.510725000000001], "7,128 cm", "above", {"color": "blue"}], [[1.489675, 2.265725], "10,846 cm", "above", {"color": "red"}]]}
- C.
{"init": {"range": [[-1.0, 8.061], [-1.0, 8.843]], "scale": [45, 45]}, "path": [[[[0.0, 7.1000000000000005], [0.0, 0.0], [7.061, 0.743], [7.061, 7.843000000000001], [0.0, 7.1000000000000005]]], [[[3.5305, 3.9215000000000004], [2.9420833333333336, 4.45125], [2.4123346830999854, 3.862832118144718], [3.0007513497666523, 3.333082118144718], [3.5305, 3.9215000000000004]]]], "line": [[[0.23666666666666666, 3.3133333333333335], [-0.23666666666666666, 3.786666666666667]], [[0.23666666666666666, 3.5500000000000003], [-0.23666666666666666, 4.023333333333333]], [[0.23666666666666666, 3.0766666666666667], [-0.23666666666666666, 3.5500000000000003]], [[0.0, 7.1000000000000005], [0.0, 0.0], {"subtype": "segment"}], [[3.7411004804420327, 0.631633926775819], [3.3198995195579672, 0.11136607322418102]], [[3.505733276833107, 0.606867203608926], [3.0845323159490414, 0.08659935005728797]], [[3.9764676840509585, 0.656400649942712], [3.555266723166893, 0.13613279639107406]], [[0.0, 0.0], [7.061, 0.743], {"subtype": "segment"}], [[7.297666666666666, 4.056333333333334], [6.824333333333334, 4.5296666666666665]], [[7.297666666666666, 4.293], [6.824333333333334, 4.766333333333333]], [[7.297666666666666, 3.819666666666667], [6.824333333333334, 4.293]], [[7.061, 0.743], [7.061, 7.843000000000001], {"subtype": "segment"}], [[3.3198995195579672, 7.211366073224181], [3.7411004804420327, 7.73163392677582]], [[3.555266723166893, 7.236132796391074], [3.9764676840509585, 7.756400649942713]], [[3.0845323159490414, 7.186599350057288], [3.505733276833107, 7.706867203608927]], [[7.061, 7.843000000000001], [0.0, 7.1000000000000005], {"subtype": "segment"}], [[0.0, 7.1000000000000005], [7.061, 0.743], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [7.061, 7.843000000000001], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.76525, 5.510750000000001], "9,501 cm", "above", {"color": "blue"}], [[1.76525, 1.9607500000000002], "10,553 cm", "above", {"color": "red"}]]}
- D.
{"init": {"range": [[-1.0, 7.500400000000001], [-1.0, 10.886800000000003]], "scale": [45, 45]}, "path": [[[[0.0, 7.080000000000002], [0.0, 0.0], [6.500400000000001, 2.8068000000000004], [6.500400000000001, 9.886800000000003], [0.0, 7.080000000000002]]], [[[3.2502000000000004, 4.943400000000001], [2.7085000000000004, 5.299500000000002], [2.3523592382964598, 4.757826797918504], [2.8940592382964603, 4.401726797918505], [3.2502000000000004, 4.943400000000001]]]], "line": [[[0.23666666666666666, 3.303333333333334], [-0.23666666666666666, 3.7766666666666677]], [[0.23666666666666666, 3.7766666666666677], [-0.23666666666666666, 3.303333333333334]], [[0.0, 7.080000000000002], [0.0, 0.0], {"subtype": "segment"}], [[3.3736592671852548, 1.7144948915818168], [3.126740732814746, 1.0923051084181836]], [[2.939105108418184, 1.5268592671852543], [3.561294891581817, 1.279940732814746]], [[0.0, 0.0], [6.500400000000001, 2.8068000000000004], {"subtype": "segment"}], [[6.737066666666667, 6.110133333333335], [6.2637333333333345, 6.583466666666668]], [[6.737066666666667, 6.583466666666668], [6.2637333333333345, 6.110133333333335]], [[6.500400000000001, 2.8068000000000004], [6.500400000000001, 9.886800000000003], {"subtype": "segment"}], [[3.126740732814746, 8.172305108418186], [3.3736592671852548, 8.79449489158182]], [[3.561294891581817, 8.35994073281475], [2.939105108418184, 8.606859267185257]], [[6.500400000000001, 9.886800000000003], [0.0, 7.080000000000002], {"subtype": "segment"}], [[0.0, 7.080000000000002], [6.500400000000001, 2.8068000000000004], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [6.500400000000001, 9.886800000000003], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.6251000000000002, 6.011700000000001], "7,776 cm", "above", {"color": "blue"}], [[1.6251000000000002, 2.4717000000000007], "11,832 cm", "above", {"color": "red"}]]}