Se repérer et se déplacer dans l'espace - 6e

Directions

Exercice 1 : Donner les directions entre les différents points pour tracer la figure

Donner les directions pour tracer la figure du point A au point E.

On indiquera les directions par leur initiales et séparées de tirets.
S-NE-SE-NO signifiera par exemple "D'abord Sud ensuite Nord-Est puis Sud-Est et enfin Nord-Ouest".

{"init": {"range": [[-1.0, 16.0], [-1.0, 16.0]], "scale": [25, 25]}, "line": [[[0.0, 0.0], [15.0, 0.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 1.0], [15.0, 1.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 2.0], [15.0, 2.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 3.0], [15.0, 3.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 4.0], [15.0, 4.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 5.0], [15.0, 5.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 6.0], [15.0, 6.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 7.0], [15.0, 7.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 8.0], [15.0, 8.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 9.0], [15.0, 9.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 10.0], [15.0, 10.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 11.0], [15.0, 11.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 12.0], [15.0, 12.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 13.0], [15.0, 13.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 14.0], [15.0, 14.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 15.0], [15.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 0.0], [0.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[1.0, 0.0], [1.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[2.0, 0.0], [2.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[3.0, 0.0], [3.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[4.0, 0.0], [4.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[5.0, 0.0], [5.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[6.0, 0.0], [6.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[7.0, 0.0], [7.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[8.0, 0.0], [8.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[9.0, 0.0], [9.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[10.0, 0.0], [10.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[11.0, 0.0], [11.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[12.0, 0.0], [12.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[13.0, 0.0], [13.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[14.0, 0.0], [14.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[15.0, 0.0], [15.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[12.0, 8.0], [3.0, 14.0], {"subtype": "segment"}], [[3.0, 14.0], [1.0, 2.0], {"subtype": "segment"}], [[1.0, 2.0], [4.0, 9.0], {"subtype": "segment"}], [[4.0, 9.0], [6.0, 3.0], {"subtype": "segment"}]], "label": [[[12.0, 8.0], "A", "above", {}], [[3.0, 14.0], "B", "above", {}], [[1.0, 2.0], "C", "above", {}], [[4.0, 9.0], "D", "above", {}], [[6.0, 3.0], "E", "above", {}]], "circle": [[[12.0, 8.0], 0.15, {"fill": "black"}], [[3.0, 14.0], 0.15, {"fill": "black"}], [[1.0, 2.0], 0.15, {"fill": "black"}], [[4.0, 9.0], 0.15, {"fill": "black"}], [[6.0, 3.0], 0.15, {"fill": "black"}]]}

Exercice 2 : Tracer un itinéraire à partir d'une séquence de directions

À partir du point \(O\) tracer l'itinéraire correspondant aux instructions suivantes :
\(S6 - E5 - N2 - O3 - N5 - O1 - N5\)

{"init": {"range": [[-7.0, 7.0], [-7.0, 7.0]], "scale": [30, 30]}, "line": [[[-6.0, -6.0], [6.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -5.0], [6.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -4.0], [6.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -3.0], [6.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -2.0], [6.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -1.0], [6.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 0.0], [6.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 1.0], [6.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 2.0], [6.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 3.0], [6.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 4.0], [6.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 5.0], [6.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 6.0], [6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -6.0], [-6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -6.0], [-5.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -6.0], [-4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -6.0], [-3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -6.0], [-2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -6.0], [-1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -6.0], [0.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -6.0], [1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -6.0], [2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -6.0], [3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -6.0], [4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -6.0], [5.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -6.0], [6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}]], "label": [[[0.0, 0.0], "O", "above left", {}]], "circle": [[[0.0, 0.0], 0.1, {}]], "drawing_options": {"tools": ["segment"]}}

Exercice 3 : Tracer un itinéraire à partir d'une séquence de directions (avec diagonales)

À partir du point \(O\) tracer l'itinéraire correspondant aux instructions suivantes :
\(E4 - S5 - NO3 - N5 - O1 - N2 - SE3\)
On considère qu'une diagonale compte pour \(\textit{1,5}\) coté de carreau

Exercice 4 : Donner les directions entre des villes sur une véritable carte (Source OpenStreeMap)

En utilisant la carte de France ci-dessous, indiquer les directions pour effectuer le parcours de villes suivant : Partir de Le Mans puis aller à Brive-la-Gaillarde, ensuite à Bourges et enfin Reims.

On indiquera les directions par leur initiales et séparées de tirets.
NE-SE-NO signifiera par exemple "Nord-Est puis Sud-Est puis Nord-Ouest".

Exercice 5 : Donner les directions entre les différents points pour tracer la figure

{"init": {"range": [[-1.0, 16.0], [-1.0, 16.0]], "scale": [25, 25]}, "line": [[[0.0, 0.0], [15.0, 0.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 1.0], [15.0, 1.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 2.0], [15.0, 2.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 3.0], [15.0, 3.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 4.0], [15.0, 4.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 5.0], [15.0, 5.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 6.0], [15.0, 6.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 7.0], [15.0, 7.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 8.0], [15.0, 8.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 9.0], [15.0, 9.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 10.0], [15.0, 10.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 11.0], [15.0, 11.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 12.0], [15.0, 12.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 13.0], [15.0, 13.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 14.0], [15.0, 14.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 15.0], [15.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[0.0, 0.0], [0.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[1.0, 0.0], [1.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[2.0, 0.0], [2.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[3.0, 0.0], [3.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[4.0, 0.0], [4.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[5.0, 0.0], [5.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[6.0, 0.0], [6.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[7.0, 0.0], [7.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[8.0, 0.0], [8.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[9.0, 0.0], [9.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[10.0, 0.0], [10.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[11.0, 0.0], [11.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[12.0, 0.0], [12.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[13.0, 0.0], [13.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[14.0, 0.0], [14.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[15.0, 0.0], [15.0, 15.0], {"subtype": "segment", "stroke": "lightgrey"}], [[2.0, 14.0], [13.0, 6.0], {"subtype": "segment"}], [[13.0, 6.0], [8.0, 13.0], {"subtype": "segment"}], [[8.0, 13.0], [9.0, 3.0], {"subtype": "segment"}], [[9.0, 3.0], [13.0, 7.0], {"subtype": "segment"}]], "label": [[[2.0, 14.0], "A", "above", {}], [[13.0, 6.0], "B", "above", {}], [[8.0, 13.0], "C", "above", {}], [[9.0, 3.0], "D", "above", {}], [[13.0, 7.0], "E", "above", {}]], "circle": [[[2.0, 14.0], 0.15, {"fill": "black"}], [[13.0, 6.0], 0.15, {"fill": "black"}], [[8.0, 13.0], 0.15, {"fill": "black"}], [[9.0, 3.0], 0.15, {"fill": "black"}], [[13.0, 7.0], 0.15, {"fill": "black"}]]}

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