Transformations - 5e

Symétries axiales

Exercice 1 : Calcul de longueurs par symétries

On considère un triangle \(EMB\) tel que \(EM = 8,5 cm\), \(EB = 4,5 cm\) et \(MB = 12 cm\).
Construire le milieu \(W\) de \([EM]\) et coder le dessin.
Construire le symétrique \(E'M'B'\) du triangle \(EMB\) par la symétrie axiale d'axe \([EM]\).

Calculer la longueur \(M'B'\).

Exercice 2 : Trouver les situations de symétrie axiale - Rectangles

Parmi les figures suivantes, lesquelles correspondent à une situation de symétrie axiale. A', B', C' et D' sont les symétriques de A, B, C et D 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"}], [[1.0, 5.0], [3.0, 5.0], {"subtype": "segment"}], [[3.0, 5.0], [3.0, 2.0], {"subtype": "segment"}], [[3.0, 2.0], [1.0, 2.0], {"subtype": "segment"}], [[1.0, 5.0], [1.0, 2.0], {"subtype": "segment"}], [[0.0, 5.0], [2.0, 5.0], {"subtype": "segment"}], [[2.0, 5.0], [2.0, 2.0], {"subtype": "segment"}], [[2.0, 2.0], [0.0, 2.0], {"subtype": "segment"}], [[0.0, 5.0], [0.0, 2.0], {"subtype": "segment"}], [[0.0, -7.0], [0.0, 7.0], {"subtype": "line"}]], "label": [[[1.0, 5.0], "A", "above left", {}], [[3.0, 5.0], "B", "above right", {}], [[3.0, 2.0], "C", "below right", {}], [[1.0, 2.0], "D", "below left", {}], [[0.0, 5.0], "A'", "above left", {}], [[2.0, 5.0], "B'", "above right", {}], [[2.0, 2.0], "C'", "below right", {}], [[0.0, 2.0], "D'", "below left", {}]]}
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"}], [[-5.0, 3.0], [4.0, 3.0], {"subtype": "segment"}], [[4.0, 3.0], [4.0, 1.0], {"subtype": "segment"}], [[4.0, 1.0], [-5.0, 1.0], {"subtype": "segment"}], [[-5.0, 3.0], [-5.0, 1.0], {"subtype": "segment"}], [[-5.0, -3.0], [4.0, -3.0], {"subtype": "segment"}], [[4.0, -3.0], [4.0, -1.0], {"subtype": "segment"}], [[4.0, -1.0], [-5.0, -1.0], {"subtype": "segment"}], [[-5.0, -3.0], [-5.0, -1.0], {"subtype": "segment"}], [[-7.0, 0.0], [7.0, 0.0], {"subtype": "line"}]], "label": [[[-5.0, 3.0], "A", "left", {}], [[4.0, 3.0], "B", "right", {}], [[4.0, 1.0], "C", "right", {}], [[-5.0, 1.0], "D", "left", {}], [[-5.0, -3.0], "A'", "left", {}], [[4.0, -3.0], "B'", "right", {}], [[4.0, -1.0], "C'", "right", {}], [[-5.0, -1.0], "D'", "left", {}]]}
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"}], [[4.0, 1.0], [3.0, 1.0], {"subtype": "segment"}], [[3.0, 1.0], [3.0, 3.0], {"subtype": "segment"}], [[3.0, 3.0], [4.0, 3.0], {"subtype": "segment"}], [[4.0, 1.0], [4.0, 3.0], {"subtype": "segment"}], [[-1.0, -4.0], [-1.0, -3.0], {"subtype": "segment"}], [[-1.0, -3.0], [-3.0, -3.0], {"subtype": "segment"}], [[-3.0, -3.0], [-3.0, -4.0], {"subtype": "segment"}], [[-1.0, -4.0], [-3.0, -4.0], {"subtype": "segment"}], [[7.0, -7.0], [-7.0, 7.0], {"subtype": "line"}]], "label": [[[4.0, 1.0], "A", "below right", {}], [[3.0, 1.0], "B", "below left", {}], [[3.0, 3.0], "C", "above left", {}], [[4.0, 3.0], "D", "above right", {}], [[-1.0, -4.0], "A'", "below right", {}], [[-1.0, -3.0], "B'", "above right", {}], [[-3.0, -3.0], "C'", "above left", {}], [[-3.0, -4.0], "D'", "below left", {}]]}
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, 4.0], [1.0, 4.0], {"subtype": "segment"}], [[1.0, 4.0], [1.0, -3.0], {"subtype": "segment"}], [[1.0, -3.0], [3.0, -3.0], {"subtype": "segment"}], [[3.0, 4.0], [3.0, -3.0], {"subtype": "segment"}], [[-3.0, 4.0], [-1.0, 4.0], {"subtype": "segment"}], [[-1.0, 4.0], [-1.0, -3.0], {"subtype": "segment"}], [[-1.0, -3.0], [-3.0, -3.0], {"subtype": "segment"}], [[-3.0, 4.0], [-3.0, -3.0], {"subtype": "segment"}], [[0.0, -7.0], [0.0, 7.0], {"subtype": "line"}]], "label": [[[3.0, 4.0], "A", "above", {}], [[1.0, 4.0], "B", "above", {}], [[1.0, -3.0], "C", "below", {}], [[3.0, -3.0], "D", "below", {}], [[-3.0, 4.0], "A'", "above", {}], [[-1.0, 4.0], "B'", "above", {}], [[-1.0, -3.0], "C'", "below", {}], [[-3.0, -3.0], "D'", "below", {}]]}

Exercice 3 : Tracer le symétrique d'un triangle par symétrie axiale

Tracer le symétrique du triangle ABC par rapport à l'axe.

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

Exercice 4 : 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": [[-7.01, 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], [1.0, 3.0], {"subtype": "segment"}], [[1.0, 3.0], [-1.0, -3.0], {"subtype": "segment"}], [[2.0, 1.0], [-1.0, -3.0], {"subtype": "segment"}], [[-6.0, 1.0], [-5.0, 3.0], {"subtype": "segment"}], [[-5.0, 3.0], [-3.0, -3.0], {"subtype": "segment"}], [[-6.0, 1.0], [-3.0, -3.0], {"subtype": "segment"}], [[-2.0, -7.0], [-2.0, 7.0], {"subtype": "line"}]], "label": [[[2.0, 1.0], "A", "above right", {}], [[1.0, 3.0], "B", "above", {}], [[-1.0, -3.0], "C", "below left", {}], [[-6.0, 1.0], "A'", "above left", {}], [[-5.0, 3.0], "B'", "above", {}], [[-3.0, -3.0], "C'", "below right", {}]], "circle": [[[2.0, 1.0], 0.01, {}], [[1.0, 3.0], 0.01, {}], [[-1.0, -3.0], 0.01, {}], [[-6.0, 1.0], 0.01, {}], [[-5.0, 3.0], 0.01, {}], [[-3.0, -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"}], [[-2.0, 3.0], [1.0, 0.0], {"subtype": "segment"}], [[1.0, 0.0], [2.0, 2.0], {"subtype": "segment"}], [[-2.0, 3.0], [2.0, 2.0], {"subtype": "segment"}], [[-5.0, 0.0], [-2.0, -3.0], {"subtype": "segment"}], [[-2.0, -3.0], [-1.0, -1.0], {"subtype": "segment"}], [[-5.0, 0.0], [-1.0, -1.0], {"subtype": "segment"}], [[6.0, -7.0], [-7.0, 6.0], {"subtype": "line"}]], "label": [[[-2.0, 3.0], "A", "above left", {}], [[1.0, 0.0], "B", "below", {}], [[2.0, 2.0], "C", "right", {}], [[-5.0, 0.0], "A'", "above left", {}], [[-2.0, -3.0], "B'", "below", {}], [[-1.0, -1.0], "C'", "right", {}]], "circle": [[[-2.0, 3.0], 0.01, {}], [[1.0, 0.0], 0.01, {}], [[2.0, 2.0], 0.01, {}], [[-5.0, 0.0], 0.01, {}], [[-2.0, -3.0], 0.01, {}], [[-1.0, -1.0], 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"}], [[1.0, 3.0], [3.0, 3.0], {"subtype": "segment"}], [[3.0, 3.0], [2.0, -3.0], {"subtype": "segment"}], [[1.0, 3.0], [2.0, -3.0], {"subtype": "segment"}], [[-1.0, 3.0], [-3.0, 3.0], {"subtype": "segment"}], [[-3.0, 3.0], [-2.0, -3.0], {"subtype": "segment"}], [[-1.0, 3.0], [-2.0, -3.0], {"subtype": "segment"}], [[0.0, -7.0], [0.0, 7.0], {"subtype": "line"}]], "label": [[[1.0, 3.0], "A", "above left", {}], [[3.0, 3.0], "B", "above right", {}], [[2.0, -3.0], "C", "below", {}], [[-1.0, 3.0], "A'", "above right", {}], [[-3.0, 3.0], "B'", "above left", {}], [[-2.0, -3.0], "C'", "below", {}]], "circle": [[[1.0, 3.0], 0.01, {}], [[3.0, 3.0], 0.01, {}], [[2.0, -3.0], 0.01, {}], [[-1.0, 3.0], 0.01, {}], [[-3.0, 3.0], 0.01, {}], [[-2.0, -3.0], 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, -3.0], [1.0, -3.0], {"subtype": "segment"}], [[1.0, -3.0], [-1.0, -1.0], {"subtype": "segment"}], [[-3.0, -3.0], [-1.0, -1.0], {"subtype": "segment"}], [[-4.0, 3.0], [0.0, 3.0], {"subtype": "segment"}], [[0.0, 3.0], [-2.0, 1.0], {"subtype": "segment"}], [[-4.0, 3.0], [-2.0, 1.0], {"subtype": "segment"}], [[-7.0, 0.0], [7.0, 0.0], {"subtype": "line"}]], "label": [[[-3.0, -3.0], "A", "left", {}], [[1.0, -3.0], "B", "right", {}], [[-1.0, -1.0], "C", "above", {}], [[-4.0, 3.0], "A'", "left", {}], [[0.0, 3.0], "B'", "right", {}], [[-2.0, 1.0], "C'", "below", {}]], "circle": [[[-3.0, -3.0], 0.01, {}], [[1.0, -3.0], 0.01, {}], [[-1.0, -1.0], 0.01, {}], [[-4.0, 3.0], 0.01, {}], [[0.0, 3.0], 0.01, {}], [[-2.0, 1.0], 0.01, {}]]}

Exercice 5 : Trouver les situations de symétrie axiale, où B est le symétrique de A par rapport à (d).

Parmi les figures suivantes, lesquelles correspondent à une situation de symétrie axiale, où B est le symétrique de A par rapport à (d).

Revenir au choix du niveau