What are the properties of rotation

In the plane, the graphic transformation of rotating a graphic by an angle around point O is called rotation, point O is called the rotation center, and the rotation angle is called the rotation angle. If point P on the graphic changes into point P after rotation ˊ, Then these two points are called the corresponding points of the rotation. Specific properties ① the distance between the corresponding points and the rotation center is equal. ② corresponding

Concept of rotation

While keeping the original shape unchanged, the figure obtained by rotating with a certain point as the center and a certain angle as the rotation angle is the figure obtained by rotating the original figure
This is the general idea of rotation in plane geometry. Solid geometry can change a fixed point into a fixed line

What is the definition and nature of rotation?

summary
Pronunciation: Xu á n Zhuan ǎ n) Rotation. English: rocendyl: in the plane, the graphic transformation of rotating a graphic by an angle around point O is called rotation, point O is called the rotation center, and the rotation angle is called the rotation angle. If point P on the graphic changes into point P after rotation ˊ, Then these two points are called the corresponding points of this rotation
nature
① the distance from the corresponding point to the rotation center is equal
② the included angle between the corresponding point and the line segment connected to the rotation center is equal to the rotation angle
③ the figures before and after rotation are all equal
Three elements
① rotation center;
② rotation direction;
③ rotation angle
Note: as long as one of the three elements is changed arbitrarily, the graphics will be different. Rotation transformation is to change from one graphics to another. In the process of change, all points on the original graphics will change the same direction and rotate the same angle around a fixed point

What is the key to translation and rotation

The key to translation is distance, and the key to rotation is center point and angle

What is the difference between translation and rotation?

Translation, rotation and axisymmetry are the three most basic transformations. A figure does not change its shape and size, but changes from one position to another. Translation is to transform a figure from one position to another. In the process of translation, the "forward direction" of each corresponding point remains parallel, Rotation is that a figure rotates around a fixed point at a certain angle. Neither rotation transformation nor translation changes the shape and size of the figure, and the distance between corresponding points remains unchanged. Therefore, such transformation is also called distance preserving transformation. Although axisymmetry also keeps the shape and size of the figure before and after transformation unchanged, But the position of the corresponding point has changed before and after the transformation. Who needs to be clear about one thing? Do what? How do you do it? To analyze translation, rotation and axisymmetry, we can also start from these aspects. To clarify translation, there are three elements: 1. Basic graphics - what graphics translate? 2. Direction: the direction in which the translation occurred; 3. Distance: how far did you translate? As shown in the first step of transformation in the figure above, triangle a of the basic figure shifts two units to the right. There are four rotating elements: 1. Basic figure - what figure rotates? 2. Rotation center - the point around which it rotates; 3. Direction: in which direction did the rotation occur, clockwise or counterclockwise? 4. Angle: how much angle did you rotate? There are two axisymmetric elements: 1. Basic graphics - what graphics are used for transformation? 2. Axis of symmetry - which line is the axis of symmetry for transformation? In the above step (4) transformation, the four basic triangles take their hypotenuse as the axis of symmetry and make axisymmetric transformation to obtain the initial figure. In teaching, students should understand the elements of the transformation. First, they should combine thinking and operation with the help of operation. For example, in the closed figure, students should put the paper pieces of triangles in square paper and move two squares upward, You can say while pushing and think while operating. Second, you should operate and learn with the help of grid paper. Grid paper presents parallel and vertical network lines, that is, you can see the direction of transformation and the distance of transformation, which is intuitive and convenient. It is convenient for students to understand the quantitative relationship in the base. By the way, the rotation center does not necessarily have to be the vertex of the basic graph. It can be the point inside the graph, Some teachers think that the rotation center is the vertex of the graph, which is not comprehensive

What are the similarities and differences between translation and rotation

Same point: the position changes, the size remains unchanged, the shape remains unchanged, and they are all in one plane
Difference: translation, motion direction unchanged
Rotation: circular motion around a point or axis

What are the properties of rotation