Chapter III Translation and Rotation of Graphics
1, definition and rules of translation
Definition of (1) translation: In a plane, a graphic moves a certain distance in a certain direction, and such graphic movement is called translation.
Key points: a. Translation does not change the shape and size of the graph (nor does it change the direction of the graph, but only changes the position of the graph).
B three elements of graphic translation: the position of the original text, the translation direction and the translation distance.
(2) Law (nature) of translation: After translation, the line segments connected by corresponding points are parallel and equal, the corresponding line segments are parallel and equal, and the corresponding angles are equal.
Note: After translation, the original text and the translated text are exactly the same.
(3) Simple translation diagram:
Attention should be paid to: ① direction; ② Distance. The whole translation drawing is to move each feature point of the whole pattern in parallel in a certain direction and a certain distance.
2. Definition and law of rotation
Definition of (1) rotation: In a plane, a figure rotates an angle around a fixed point in a certain direction, and such a figure movement is called circular rotation. This fixed point is called the center of rotation; The angle of rotation is called the rotation angle.
Key: A. Rotation does not change the shape and size of the graph (but it will change the direction of the graph and also change the position of the graph).
B Four elements of graphic rotation: original position, rotation center, rotation direction and rotation angle.
(2) the law of rotation (natural):
After rotation, every point on the graph rotates around the rotation center at the same angle and in the same direction. The angle formed by the connecting line of any pair of corresponding points and the rotation center is the rotation angle, and the distances from the corresponding points to the rotation center are equal. (Before and after the rotation, the corresponding line segments of the two pictures are equal, and the corresponding angles are equal. )
Note: After rotation, the original graph and the rotated graph are the same.
(3) Simple rotation drawing:
Attention should be paid to the drawing of rotation: ① the direction of rotation; ② Rotation angle. The whole rotation painting is to rotate and move every feature point of the whole pattern around the rotation center in a certain rotation direction and angle.
3. Analysis and design of the model
(1) First find the basic pattern, and then analyze the relationship between other patterns and it, that is, what kind of motion transformation it makes.
② The basic means of pattern design mainly include: axial symmetry, translation and rotation.
4. Axisymmetric knowledge review
(1) Definition of an axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, then the figure is called an axisymmetric figure. The straight line where the crease lies is called the symmetry axis.
(2) Two figures form an axis symmetry: for two figures, if they can completely overlap after being folded in half along a straight line, then the two figures form an axis symmetry, and this straight line is the axis symmetry.
(3) Note:
① Axisymmetry refers to the positional relationship between two graphs; Axisymmetric graph is a kind of graph with special shape.
(2) Two symmetrical figures must be congruent figures.
(4) Axisymmetry: the line segments connected by corresponding points are vertically bisected by the axis of symmetry; The corresponding line segments are equal; The corresponding angles are equal.
(3) Simple axisymmetric drawing:
Finding a figure whose geometric figure is symmetrical about a straight line can be transformed into finding a point whose characteristic point is symmetrical about this straight line. Then connect the feature points in turn.
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