Transformations - 5e

Symétries centrales

Exercice 1 : Construire le symétrique d'un point, d'un segment et d'une droite

Tracer le symétrique du point C, du segment [AB] et de la droite (d) par rapport au point O.

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Exercice 2 : Tracer le symétrique d'un triangle par symétrie centrale

Tracer le symétrique du triangle ABC par rapport à O.

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Exercice 3 : Placer le centre de symétrie d'une figure, si existant

Placer le centre de symétrie de la figure suivante si elle en possède un. Dans le cas contraire, valider sans aucun point.

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Exercice 4 : Trouver les situations de symétrie centrale - Triangles

Parmi les figures suivantes, la ou lesquelles correspondent à une situation de symétrie centrale de centre \(O\) ?
A', B' et C' sont les symétriques de A, B et C respectivement par rapport à O.

A.

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B.

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C.

{"init": {"range": [[-7.0, 7.0], [-7.0, 7.0]], "scale": [40, 40]}, "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"}], [[0.0, -3.0], [3.0, -1.0], {"subtype": "segment"}], [[3.0, -1.0], [-3.0, -2.0], {"subtype": "segment"}], [[0.0, -3.0], [-3.0, -2.0], {"subtype": "segment"}], [[0.0, 3.0], [-3.0, 1.0], {"subtype": "segment"}], [[-3.0, 1.0], [3.0, 2.0], {"subtype": "segment"}], [[0.0, 3.0], [3.0, 2.0], {"subtype": "segment"}]], "label": [[[0.0, -3.0], "A", "below", {}], [[3.0, -1.0], "B", "right", {}], [[-3.0, -2.0], "C", "left", {}], [[0.0, 3.0], "A'", "above", {}], [[-3.0, 1.0], "B'", "left", {}], [[3.0, 2.0], "C'", "right", {}], [[0.0, 0.0], "O", "above", {}]], "circle": [[[0.0, -3.0], 0.01, {}], [[3.0, -1.0], 0.01, {}], [[-3.0, -2.0], 0.01, {}], [[0.0, 3.0], 0.01, {}], [[-3.0, 1.0], 0.01, {}], [[3.0, 2.0], 0.01, {}], [[0.0, 0.0], 0.01, {}]]}
D.

{"init": {"range": [[-7.0, 7.0], [-7.0, 7.0]], "scale": [40, 40]}, "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"}], [[1.0, 2.0], [3.0, -1.0], {"subtype": "segment"}], [[3.0, -1.0], [-2.0, 2.0], {"subtype": "segment"}], [[1.0, 2.0], [-2.0, 2.0], {"subtype": "segment"}], [[-3.0, 1.0], [2.0, -2.0], {"subtype": "segment"}], [[2.0, -2.0], [-1.0, -2.0], {"subtype": "segment"}], [[-3.0, 1.0], [-1.0, -2.0], {"subtype": "segment"}]], "label": [[[1.0, 2.0], "A", "above", {}], [[3.0, -1.0], "B", "below right", {}], [[-2.0, 2.0], "C", "left", {}], [[-3.0, 1.0], "A'", "above left", {}], [[2.0, -2.0], "B'", "right", {}], [[-1.0, -2.0], "C'", "below", {}], [[0.0, 0.0], "O", "above", {}]], "circle": [[[1.0, 2.0], 0.01, {}], [[3.0, -1.0], 0.01, {}], [[-2.0, 2.0], 0.01, {}], [[-3.0, 1.0], 0.01, {}], [[2.0, -2.0], 0.01, {}], [[-1.0, -2.0], 0.01, {}], [[0.0, 0.0], 0.01, {}]]}

Exercice 5 : Reconnaître le symétrique centrale d'une image

Dans les trois figures ci-dessous, trouver celle qui représente l'image et son symétrique par rapport au point O.
A.

Revenir au choix du niveau