Transformations - 4e

Rotations

Exercice 1 : Identifier un triangle équilatéral après rotation.

Trouver la ou les figures dans lesquelles \( A'B'C' \) est l'image du triangle \( ABC \) par la rotation de centre \( O \) suivant un angle de \( 270 °\) dans le sens des aiguilles d'une montre.

Exercice 2 : Image de point par rotation dans une grille de triangles équilatéraux (angles inférieurs à 180°

On s’intéresse à la figure ci-dessous composée de triangles équilatéraux :

Compléter les phrases suivantes :

H est l’image de par la rotation de centre J d’angle 180° dans le sens antihoraire.

G est l’image de K par la rotation de centre d’angle 60° dans le sens antihoraire.

est l’image de L par la rotation de centre K d’angle 120° dans le sens horaire.

Exercice 3 : Tracer l'image d'un triangle par une rotation (90°, 180° ou 270°)

Tracer l'image du triangle \(ABC\) par la rotation de \(180 °\) dans le sens antihoraire de centre \(O\).

{"drawing_options": {"tools": ["segment"]}, "label": [[[2.0, 3.0], "A", "above", {}], [[0.0, -1.0], "B", "below left", {}], [[5.0, 4.0], "C", "above right", {}], [[0.0, 0.0], "O", "above", {}]], "init": {"range": [[-10, 10], [-10, 10]], "scale": [30, 30]}, "line": [[[-10.0, -10.0], [10.0, -10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -9.0], [10.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -8.0], [10.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -7.0], [10.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -6.0], [10.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -5.0], [10.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -4.0], [10.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -3.0], [10.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -2.0], [10.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -1.0], [10.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 0.0], [10.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 1.0], [10.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 8.0], [10.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 9.0], [10.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -10.0], [-10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -10.0], [-9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -10.0], [-8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -10.0], [-7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -10.0], [-6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -10.0], [-5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -10.0], [-4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -10.0], [-3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -10.0], [-2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -10.0], [-1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -10.0], [0.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -10.0], [1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -10.0], [2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -10.0], [3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -10.0], [4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -10.0], [5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -10.0], [6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -10.0], [7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -10.0], [8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -10.0], [9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, -10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, 3.0], [0.0, -1.0], {"subtype": "segment"}], [[0.0, -1.0], [5.0, 4.0], {"subtype": "segment"}], [[2.0, 3.0], [5.0, 4.0], {"subtype": "segment"}]], "circle": [[[2.0, 3.0], 0.2, {"fill": "black"}], [[0.0, -1.0], 0.2, {"fill": "black"}], [[5.0, 4.0], 0.2, {"fill": "black"}], [[0.0, 0.0], 0.2, {"fill": "black"}]]}

Exercice 4 : Tracer l'image d'un point par une rotation (90°, 180° ou 270°)

Tracer l'image du point \(F\) par la rotation de \(270 °\) dans le sens antihoraire de centre \(O\).

{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30, 30]}, "line": [[[-10.0, -10.0], [10.0, -10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -9.0], [10.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -8.0], [10.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -7.0], [10.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -6.0], [10.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -5.0], [10.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -4.0], [10.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -3.0], [10.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -2.0], [10.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -1.0], [10.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 0.0], [10.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 1.0], [10.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 8.0], [10.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 9.0], [10.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -10.0], [-10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -10.0], [-9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -10.0], [-8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -10.0], [-7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -10.0], [-6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -10.0], [-5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -10.0], [-4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -10.0], [-3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -10.0], [-2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -10.0], [-1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -10.0], [0.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -10.0], [1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -10.0], [2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -10.0], [3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -10.0], [4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -10.0], [5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -10.0], [6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -10.0], [7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -10.0], [8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -10.0], [9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, -10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}]], "label": [[[0.0, 2.0], "F", "above", {}], [[0.0, 0.0], "O", "above", {}]], "circle": [[[0.0, 2.0], 0.2, {"fill": "black"}], [[0.0, 0.0], 0.2, {"fill": "black"}]], "drawing_options": {"tools": ["point"]}}

Exercice 5 : Tracer l'image d'un quadrilatère par une rotation (90°, 180° ou 270°)

Tracer l'image du quadrilatère \(ABCD\) par la rotation de \(270°\) dans le sens horaire de centre \(O\).

{"init": {"range": [[-10, 10], [-10, 10]], "scale": [30, 30]}, "line": [[[-10.0, -10.0], [10.0, -10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -9.0], [10.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -8.0], [10.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -7.0], [10.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -6.0], [10.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -5.0], [10.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -4.0], [10.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -3.0], [10.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -2.0], [10.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -1.0], [10.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 0.0], [10.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 1.0], [10.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 8.0], [10.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 9.0], [10.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, 10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -10.0], [-10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -10.0], [-9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -10.0], [-8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -10.0], [-7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -10.0], [-6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -10.0], [-5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -10.0], [-4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -10.0], [-3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -10.0], [-2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -10.0], [-1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -10.0], [0.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -10.0], [1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -10.0], [2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -10.0], [3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -10.0], [4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -10.0], [5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -10.0], [6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -10.0], [7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -10.0], [8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -10.0], [9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, -10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, 5.0], [1.0, 5.0], {"subtype": "segment"}], [[1.0, 5.0], [5.0, 1.0], {"subtype": "segment"}], [[5.0, 1.0], [-3.0, -5.0], {"subtype": "segment"}], [[-3.0, -5.0], [-5.0, 5.0], {"subtype": "segment"}]], "circle": [[[-5.0, 5.0], 0.2, {"fill": "black"}], [[1.0, 5.0], 0.2, {"fill": "black"}], [[5.0, 1.0], 0.2, {"fill": "black"}], [[-3.0, -5.0], 0.2, {"fill": "black"}], [[0.0, 0.0], 0.2, {"fill": "black"}]], "label": [[[-5.0, 5.0], "A", "above left", {}], [[1.0, 5.0], "B", "above right", {}], [[5.0, 1.0], "C", "right", {}], [[-3.0, -5.0], "D", "below", {}], [[0.0, 0.0], "O", "above", {}]], "drawing_options": {"tools": ["segment"]}}

Revenir au choix du niveau