L’espace - 4e

Repérage dans un pavé droit

Exercice 1 : Se repérer dans un pavé droit

On représente le pavé droit \( ABCDEFGH \) dans le repère d'origine \( A \) ci-dessous.

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Donner les coordonnées du point \( A \).
On donnera la réponse sous la forme \( (x;y;z) \), par exemple \( (2;2;1) \).

Donner les coordonnées du point \( H \).
On donnera la réponse sous la forme \( (x;y;z) \), par exemple \( (2;2;1) \).

Sachant que \( L ∈ [CD] \), donner les coordonnées du point \( L \).
On donnera la réponse sous la forme \( (x;y;z) \), par exemple \( (2;2;1) \).

Placer le point de coordonnées \( ( 0 ; 0 ; 2 ) \)

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[[-5.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 8.0], [10.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 9.0], [10.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 0.0], [0.0, 9.0], {"subtype": "segment", "arrow-end": "classic-wide-long", "opacity": 0.5}], [[0.0, 0.0], [10.0, 0.0], {"subtype": "segment", "arrow-end": "classic-wide-long", "opacity": 0.5}], [[0.0, 0.0], [-5.0, -10.0], {"subtype": "segment", "arrow-end": "classic-wide-long", "opacity": 0.5}], [[0.0, 0.0], [8.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [0.0, 6.0], {"subtype": "segment"}], [[0.0, 0.0], [-3.0, -6.0], 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"segment", "opacity": 0.5}], [[-0.8, -2.1], [-1.2, -1.9], {"subtype": "segment", "opacity": 0.5}], [[-1.8, -4.1], [-2.2, -3.9], {"subtype": "segment", "opacity": 0.5}], [[-2.8, -6.1], [-3.2, -5.9], {"subtype": "segment", "opacity": 0.5}], [[-3.8, -8.1], [-4.2, -7.9], {"subtype": "segment", "opacity": 0.5}], [[-4.8, -10.1], [-5.2, -9.9], {"subtype": "segment", "opacity": 0.5}], [[-5.8, -12.1], [-6.2, -11.9], {"subtype": "segment", "opacity": 0.5}], [[-6.8, -14.1], [-7.2, -13.9], {"subtype": "segment", "opacity": 0.5}], [[-7.8, -16.1], [-8.2, -15.9], {"subtype": "segment", "opacity": 0.5}], [[-8.8, -18.1], [-9.2, -17.9], {"subtype": "segment", "opacity": 0.5}], [[-0.2, 0.0], [0.2, 0.0], {"subtype": "segment", "stroke": "#6495ED"}], [[0.0, -0.2], [0.0, 0.2], {"subtype": "segment", "stroke": "#6495ED"}], [[-3.2, -6.0], [-2.8, -6.0], {"subtype": "segment", "stroke": "#6495ED"}], [[-3.0, -6.2], [-3.0, -5.8], {"subtype": "segment", "stroke": "#6495ED"}], [[4.8, -6.0], [5.2, -6.0], {"subtype": 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Exercice 2 : Lire les coordonnées d'un point dans un plan 3D

Dans le repère ci-dessous, donner les coordonnées du point M sous la forme \((x ; y ; z)\).

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"z": 0.0}, "label_render": {"color": 204}}, "Point3D_98": {"type": "Point", "position": {"x": 36.0, "y": 0.0, "z": 42.0}, "point_render": {"color": 204}, "label_render": {"visible": false}}, "Point3D_99": {"type": "Point", "position": {"x": 36.0, "y": 12.0, "z": 0.0}, "point_render": {"color": 204}, "label_render": {"visible": false}}, "Point3D_100": {"type": "Point", "position": {"x": 0.0, "y": 12.0, "z": 42.0}, "point_render": {"color": 204}, "label_render": {"visible": false}}, "Segment3D_101": {"type": "Segment", "pt1": {"x": 36.0, "y": 12.0, "z": 42.0}, "pt2": {"x": 36.0, "y": 0.0, "z": 42.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"color": 204, "dashed": true}}, "Segment3D_102": {"type": "Segment", "pt1": {"x": 36.0, "y": 12.0, "z": 42.0}, "pt2": {"x": 36.0, "y": 12.0, "z": 0.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"color": 204, "dashed": true}}, "Segment3D_103": {"type": "Segment", "pt1": {"x": 36.0, "y": 12.0, "z": 42.0}, "pt2": {"x": 0.0, "y": 12.0, "z": 42.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"color": 204, "dashed": true}}}}

Exercice 3 : Indiquer si un entier n (entre 101 et 1000) est divisible par 2, 3, 5, 9, 10

Exercice 4 : Se repérer dans un pavé droit

On représente le pavé droit \( ABCDEFGH \) dans le repère d'origine \( A \) ci-dessous.

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Donner les coordonnées du point \( A \).
On donnera la réponse sous la forme \( (x;y;z) \), par exemple \( (2;2;1) \).

Donner les coordonnées du point \( H \).
On donnera la réponse sous la forme \( (x;y;z) \), par exemple \( (2;2;1) \).

Sachant que \( L ∈ [AE] \), donner les coordonnées du point \( L \).
On donnera la réponse sous la forme \( (x;y;z) \), par exemple \( (2;2;1) \).

Placer le point de coordonnées \( ( 1 ; 4 ; 2 ) \)

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-11.0], [8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -11.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -10.0], [10.0, -10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -9.0], [10.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -8.0], [10.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -7.0], [10.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -6.0], [10.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -5.0], [10.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -4.0], [10.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -3.0], [10.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -2.0], [10.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -1.0], [10.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 0.0], [10.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 1.0], [10.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 8.0], [10.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 9.0], [10.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 0.0], [0.0, 9.0], {"subtype": "segment", "arrow-end": "classic-wide-long", "opacity": 0.5}], [[0.0, 0.0], [10.0, 0.0], {"subtype": "segment", "arrow-end": "classic-wide-long", "opacity": 0.5}], [[0.0, 0.0], [-5.0, -10.0], {"subtype": "segment", "arrow-end": "classic-wide-long", "opacity": 0.5}], [[0.0, 0.0], [8.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [0.0, 4.0], {"subtype": "segment"}], [[0.0, 0.0], [-2.0, -4.0], {"subtype": "segment"}], [[8.0, 0.0], [8.0, 4.0], {"subtype": "segment"}], [[8.0, 0.0], [6.0, -4.0], {"subtype": "segment"}], [[6.0, -4.0], [6.0, 0.0], {"subtype": "segment"}], [[6.0, -4.0], [-2.0, -4.0], {"subtype": "segment"}], [[-2.0, -4.0], [-2.0, 0.0], {"subtype": "segment"}], [[-2.0, 0.0], [6.0, 0.0], {"subtype": "segment"}], [[-2.0, 0.0], [0.0, 4.0], {"subtype": "segment"}], [[0.0, 4.0], [8.0, 4.0], {"subtype": "segment"}], [[8.0, 4.0], [6.0, 0.0], {"subtype": "segment"}], [[2.0, -0.2], [2.0, 0.2], {"subtype": "segment", "opacity": 0.5}], [[4.0, -0.2], [4.0, 0.2], {"subtype": "segment", "opacity": 0.5}], [[6.0, -0.2], [6.0, 0.2], {"subtype": "segment", "opacity": 0.5}], [[8.0, -0.2], [8.0, 0.2], {"subtype": "segment", "opacity": 0.5}], [[-0.2, 2.0], [0.2, 2.0], {"subtype": "segment", "opacity": 0.5}], [[-0.2, 4.0], [0.2, 4.0], {"subtype": "segment", "opacity": 0.5}], [[-0.2, 6.0], [0.2, 6.0], {"subtype": "segment", "opacity": 0.5}], [[-0.2, 8.0], [0.2, 8.0], {"subtype": "segment", "opacity": 0.5}], [[-0.8, -2.1], [-1.2, -1.9], {"subtype": "segment", "opacity": 0.5}], [[-1.8, -4.1], [-2.2, -3.9], {"subtype": "segment", "opacity": 0.5}], [[-2.8, -6.1], [-3.2, -5.9], {"subtype": "segment", "opacity": 0.5}], [[-3.8, -8.1], [-4.2, -7.9], {"subtype": "segment", "opacity": 0.5}], [[-4.8, -10.1], [-5.2, -9.9], {"subtype": "segment", "opacity": 0.5}], [[-5.8, -12.1], [-6.2, -11.9], {"subtype": "segment", "opacity": 0.5}], [[-6.8, -14.1], [-7.2, -13.9], {"subtype": "segment", "opacity": 0.5}], [[-7.8, -16.1], [-8.2, -15.9], {"subtype": "segment", "opacity": 0.5}], [[-8.8, -18.1], [-9.2, -17.9], {"subtype": "segment", "opacity": 0.5}], [[-0.2, 0.0], [0.2, 0.0], {"subtype": "segment", "stroke": "#6495ED"}], [[0.0, -0.2], [0.0, 0.2], {"subtype": "segment", "stroke": "#6495ED"}], [[-2.2, -4.0], [-1.8, -4.0], {"subtype": "segment", "stroke": "#6495ED"}], [[-2.0, -4.2], [-2.0, -3.8], {"subtype": "segment", "stroke": "#6495ED"}], [[5.8, -4.0], [6.2, -4.0], {"subtype": "segment", "stroke": "#6495ED"}], [[6.0, -4.2], [6.0, -3.8], {"subtype": "segment", "stroke": "#6495ED"}], [[7.8, 0.0], [8.2, 0.0], {"subtype": "segment", "stroke": "#6495ED"}], [[8.0, -0.2], [8.0, 0.2], {"subtype": "segment", "stroke": "#6495ED"}], [[-0.2, 4.0], [0.2, 4.0], {"subtype": "segment", "stroke": "#6495ED"}], [[0.0, 3.8], [0.0, 4.2], {"subtype": "segment", "stroke": "#6495ED"}], [[-2.2, 0.0], [-1.8, 0.0], {"subtype": "segment", "stroke": "#6495ED"}], [[-2.0, -0.2], [-2.0, 0.2], {"subtype": "segment", "stroke": "#6495ED"}], [[5.8, 0.0], [6.2, 0.0], {"subtype": "segment", "stroke": "#6495ED"}], [[6.0, -0.2], [6.0, 0.2], {"subtype": "segment", "stroke": "#6495ED"}], [[7.8, 4.0], [8.2, 4.0], {"subtype": "segment", "stroke": "#6495ED"}], [[8.0, 3.8], [8.0, 4.2], {"subtype": "segment", "stroke": "#6495ED"}], [[-0.2, 2.0], [0.2, 2.0], {"subtype": "segment", "stroke": "#6495ED"}], [[0.0, 1.8], [0.0, 2.2], {"subtype": "segment", "stroke": "#6495ED"}]], "label": [[[0.0, 0.0], "0", "below", {}], [[2.0, 0.0], "1", "below", {}], [[0.0, 2.0], "1", "left", {}], [[-1.0, -2.0], "1", "left", {}], [[0.0, 0.0], "A", "above", {}], [[-2.0, -4.0], "B", "above", {}], [[6.0, -4.0], "C", "above", {}], [[8.0, 0.0], "D", "above", {}], [[0.0, 4.0], "E", "above", {}], [[-2.0, 0.0], "F", "above", {}], [[6.0, 0.0], "G", "above", {}], [[8.0, 4.0], "H", "above", {}], [[0.0, 2.0], "L", "above", {}], [[9.0, 0.0], "y", "above", {"color": "#8BC63E"}], [[-3.0, -9.0], "x", "above", {"color": "#8BC63E"}], [[1.0, 8.0], "z", "above", {"color": "#8BC63E"}]], "drawing_options": {"tools": ["point"], "style": {"point": {"radius": 0.3, "snapToGrid": [1, 1]}}}}

Exercice 5 : Lire les coordonnées d'un point dans un plan 3D

Dans le repère ci-dessous, donner les coordonnées du point M sous la forme \((x ; y ; z)\).

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