Symétrie axiale - 6e

Symétrie axiale

Exercice 1 : Tracer les symétries axiale d'une figure

Compléter le schéma afin que les droites \( (d1) \) et \( (d2) \) soient des axes de symétrie de la figure.
On n'ajoutera pas d'élément dans la partie contenant la figure initiale.

{"init": {"range": [[-7.0, 7.0], [-7.0, 7.0]], "scale": [30, 30]}, "circle": [[[0.0, 1.0], 0.3, {"fill": "blue", "stroke": "blue"}], [[2.0, 3.0], 0.3, {"fill": "blue", "stroke": "blue"}], [[3.0, 2.0], 0.3, {"fill": "blue", "stroke": "blue"}], [[1.0, 0.0], 0.3, {"fill": "blue", "stroke": "blue"}]], "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, 1.0], [2.0, 3.0], {"subtype": "segment", "stroke": "blue"}], [[2.0, 3.0], [3.0, 2.0], {"subtype": "segment", "stroke": "blue"}], [[3.0, 2.0], [1.0, 0.0], {"subtype": "segment", "stroke": "blue"}], [[-7.0, 0.0], [6.5, 0.0], {"subtype": "line"}], [[0.0, -7.0], [0.0, 6.5], {"subtype": "line"}]], "label": [[[7.0, 0.0], "(d2)", {"subtype": "line"}], [[0.0, 7.0], "(d1)", {"subtype": "line"}]], "optional": {"init": {"range": [[-1.3, 4.3], [-1.3, 4.3]], "scale": [30, 30]}, "circle": [[[0.0, 1.0], 0.3, {"fill": "blue", "stroke": "blue"}], [[2.0, 3.0], 0.3, {"fill": "blue", "stroke": "blue"}], [[3.0, 2.0], 0.3, {"fill": "blue", "stroke": "blue"}], [[1.0, 0.0], 0.3, {"fill": "blue", "stroke": "blue"}]], "line": [[[0.0, 1.0], [2.0, 3.0], {"subtype": "segment", "stroke": "blue"}], [[2.0, 3.0], [3.0, 2.0], {"subtype": "segment", "stroke": "blue"}], [[3.0, 2.0], [1.0, 0.0], {"subtype": "segment", "stroke": "blue"}]]}, "drawing_options": {"tools": ["segment"]}}

Exercice 2 : Trouver les situations de symétrie axiale - Triangles

Parmi les figures suivantes, lesquelles correspondent à une situation de symétrie axiale. A', B' et C' sont les symétriques de A, B et C respectivement par rapport à l'axe.

A.

{"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"}], [[-2.0, 1.0], [-2.0, -2.0], {"subtype": "segment"}], [[-2.0, -2.0], [0.0, 3.0], {"subtype": "segment"}], [[-2.0, 1.0], [0.0, 3.0], {"subtype": "segment"}], [[2.0, 1.0], [2.0, -2.0], {"subtype": "segment"}], [[2.0, -2.0], [4.0, 3.0], {"subtype": "segment"}], [[2.0, 1.0], [4.0, 3.0], {"subtype": "segment"}], [[1.0, -7.0], [1.0, 7.0], {"subtype": "line"}]], "label": [[[-2.0, 1.0], "A", "above left", {}], [[-2.0, -2.0], "B", "below", {}], [[0.0, 3.0], "C", "above right", {}], [[2.0, 1.0], "A'", "above left", {}], [[2.0, -2.0], "B'", "below", {}], [[4.0, 3.0], "C'", "above right", {}]], "circle": [[[-2.0, 1.0], 0.01, {}], [[-2.0, -2.0], 0.01, {}], [[0.0, 3.0], 0.01, {}], [[2.0, 1.0], 0.01, {}], [[2.0, -2.0], 0.01, {}], [[4.0, 3.0], 0.01, {}]]}
B.

{"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"}], [[3.0, 3.0], [3.0, 0.0], {"subtype": "segment"}], [[3.0, 0.0], [5.0, -5.0], {"subtype": "segment"}], [[3.0, 3.0], [5.0, -5.0], {"subtype": "segment"}], [[1.0, 3.0], [1.0, 0.0], {"subtype": "segment"}], [[1.0, 0.0], [-1.0, -5.0], {"subtype": "segment"}], [[1.0, 3.0], [-1.0, -5.0], {"subtype": "segment"}], [[2.0, 7.0], [2.0, -7.0], {"subtype": "line"}]], "label": [[[3.0, 3.0], "A", "above", {}], [[3.0, 0.0], "B", "above left", {}], [[5.0, -5.0], "C", "below", {}], [[1.0, 3.0], "A'", "above", {}], [[1.0, 0.0], "B'", "above right", {}], [[-1.0, -5.0], "C'", "below", {}]], "circle": [[[3.0, 3.0], 0.01, {}], [[3.0, 0.0], 0.01, {}], [[5.0, -5.0], 0.01, {}], [[1.0, 3.0], 0.01, {}], [[1.0, 0.0], 0.01, {}], [[-1.0, -5.0], 0.01, {}]]}
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"}], [[-3.0, 1.0], [0.0, 2.0], {"subtype": "segment"}], [[0.0, 2.0], [2.0, 4.0], {"subtype": "segment"}], [[-3.0, 1.0], [2.0, 4.0], {"subtype": "segment"}], [[2.0, -4.0], [3.0, -1.0], {"subtype": "segment"}], [[3.0, -1.0], [5.0, 1.0], {"subtype": "segment"}], [[2.0, -4.0], [5.0, 1.0], {"subtype": "segment"}], [[7.0, 6.0], [-6.0, -7.0], {"subtype": "line"}]], "label": [[[-3.0, 1.0], "A", "below left", {}], [[0.0, 2.0], "B", "below right", {}], [[2.0, 4.0], "C", "above right", {}], [[2.0, -4.0], "A'", "below left", {}], [[3.0, -1.0], "B'", "above left", {}], [[5.0, 1.0], "C'", "above right", {}]], "circle": [[[-3.0, 1.0], 0.01, {}], [[0.0, 2.0], 0.01, {}], [[2.0, 4.0], 0.01, {}], [[2.0, -4.0], 0.01, {}], [[3.0, -1.0], 0.01, {}], [[5.0, 1.0], 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"}], [[3.0, -1.0], [1.0, 0.0], {"subtype": "segment"}], [[1.0, 0.0], [-3.0, 5.0], {"subtype": "segment"}], [[3.0, -1.0], [-3.0, 5.0], {"subtype": "segment"}], [[0.0, -3.0], [-1.0, -2.0], {"subtype": "segment"}], [[-1.0, -2.0], [-5.0, 2.0], {"subtype": "segment"}], [[0.0, -3.0], [-5.0, 2.0], {"subtype": "segment"}], [[6.0, -7.0], [-7.0, 6.0], {"subtype": "line"}]], "label": [[[3.0, -1.0], "A", "below right", {}], [[1.0, 0.0], "B", "below right", {}], [[-3.0, 5.0], "C", "above left", {}], [[0.0, -3.0], "A'", "below right", {}], [[-1.0, -2.0], "B'", "below right", {}], [[-5.0, 2.0], "C'", "above left", {}]], "circle": [[[3.0, -1.0], 0.01, {}], [[1.0, 0.0], 0.01, {}], [[-3.0, 5.0], 0.01, {}], [[0.0, -3.0], 0.01, {}], [[-1.0, -2.0], 0.01, {}], [[-5.0, 2.0], 0.01, {}]]}

Exercice 3 : Tracer les axes de symétrie d'une figure simple

Tracer le ou les axes de symétrie de la figure suivante.

Exercice 4 : Trouver les situations de symétrie axiale - Segments

Parmi les figures suivantes, la ou lesquelles correspondent à une situation de symétrie axiale. A' et B' sont les symétriques de A et B respectivement par rapport à l'axe ?

A.

{"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, -1.0], [0.0, 0.0], {"subtype": "segment"}], [[-3.0, 2.0], [-2.0, 2.0], {"subtype": "segment"}], [[-7.0, -5.0], [5.0, 7.0], {"subtype": "line"}]], "label": [[[0.0, -1.0], "A", "below", {}], [[0.0, 0.0], "B", "above", {}], [[-3.0, 2.0], "A'", "left", {}], [[-2.0, 2.0], "B'", "right", {}]], "circle": [[[0.0, -1.0], 0.01, {}], [[0.0, 0.0], 0.01, {}], [[-3.0, 2.0], 0.01, {}], [[-2.0, 2.0], 0.01, {}]]}
B.

{"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"}], [[2.0, -2.0], [-1.0, 0.0], {"subtype": "segment"}], [[4.0, 0.0], [2.0, 3.0], {"subtype": "segment"}], [[7.0, -5.0], [-5.0, 7.0], {"subtype": "line"}]], "label": [[[2.0, -2.0], "A", "below right", {}], [[-1.0, 0.0], "B", "above left", {}], [[4.0, 0.0], "A'", "below right", {}], [[2.0, 3.0], "B'", "above left", {}]], "circle": [[[2.0, -2.0], 0.01, {}], [[-1.0, 0.0], 0.01, {}], [[4.0, 0.0], 0.01, {}], [[2.0, 3.0], 0.01, {}]]}
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"}], [[2.0, 1.0], [2.0, 2.0], {"subtype": "segment"}], [[-1.0, -2.0], [-2.0, -2.0], {"subtype": "segment"}], [[7.0, -7.0], [-7.0, 7.0], {"subtype": "line"}]], "label": [[[2.0, 1.0], "A", "below", {}], [[2.0, 2.0], "B", "above", {}], [[-1.0, -2.0], "A'", "right", {}], [[-2.0, -2.0], "B'", "left", {}]], "circle": [[[2.0, 1.0], 0.01, {}], [[2.0, 2.0], 0.01, {}], [[-1.0, -2.0], 0.01, {}], [[-2.0, -2.0], 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"}], [[0.0, 0.0], [1.0, 2.0], {"subtype": "segment"}], [[0.0, -2.0], [1.0, -4.0], {"subtype": "segment"}], [[7.0, -1.0], [-7.0, -1.0], {"subtype": "line"}]], "label": [[[0.0, 0.0], "A", "below left", {}], [[1.0, 2.0], "B", "above right", {}], [[1.0, -4.0], "A'", "below right", {}], [[0.0, -2.0], "B'", "above left", {}]], "circle": [[[0.0, 0.0], 0.01, {}], [[1.0, 2.0], 0.01, {}], [[1.0, -4.0], 0.01, {}], [[0.0, -2.0], 0.01, {}]]}

Exercice 5 : Tracer les symétriques de points

Construire les symétriques des points A, B, C et D par rapport à l'axe \((d)\).

{"init": {"range": [[-9.0, 9.0], [-9.0, 9.0]], "scale": [30, 30]}, "line": [[[-8.0, -8.0], [8.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -7.0], [8.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -6.0], [8.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -5.0], [8.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -4.0], [8.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -3.0], [8.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -2.0], [8.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -1.0], [8.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 0.0], [8.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 1.0], [8.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 2.0], [8.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 3.0], [8.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 4.0], [8.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 5.0], [8.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 6.0], [8.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 7.0], [8.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, 8.0], [8.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -8.0], [-8.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -8.0], [-7.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -8.0], [-6.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -8.0], [-5.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -8.0], [-4.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -8.0], [-3.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -8.0], [-2.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -8.0], [-1.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -8.0], [0.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -8.0], [1.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -8.0], [2.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -8.0], [3.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -8.0], [4.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -8.0], [5.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -8.0], [6.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -8.0], [7.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -8.0], [8.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -9.0], [-8.646446609406727, 8.646446609406727], {"subtype": "line"}]], "label": [[[-3.0, -3.0], "A", "above", {}], [[-6.0, 6.0], "B", "above", {}], [[4.0, -2.0], "C", "above", {}], [[2.0, -6.0], "D", "above", {}], [[-9.0, 9.0], "(d)", {"subtype": "line"}]], "circle": [[[-3.0, -3.0], 0.3, {"stroke": "blue"}], [[-6.0, 6.0], 0.3, {"stroke": "blue"}], [[4.0, -2.0], 0.3, {"stroke": "blue"}], [[2.0, -6.0], 0.3, {"stroke": "blue"}]], "optional": {"init": {"range": [[-7.3, 5.3], [-7.3, 7.3]], "scale": [30, 30]}, "label": [[[-3.0, -3.0], "A", "above", {}], [[-6.0, 6.0], "B", "above", {}], [[4.0, -2.0], "C", "above", {}], [[2.0, -6.0], "D", "above", {}]], "circle": [[[-3.0, -3.0], 0.3, {"stroke": "blue"}], [[-6.0, 6.0], 0.3, {"stroke": "blue"}], [[4.0, -2.0], 0.3, {"stroke": "blue"}], [[2.0, -6.0], 0.3, {"stroke": "blue"}]]}, "drawing_options": {"tools": ["point"]}}

Revenir au choix du niveau