1, the formula of symmetry point in senior high school mathematics is an important concept in mathematics, which describes how to calculate the symmetry point of a point about another specific point given the position of a point in a plane rectangular coordinate system. This concept has a wide range of applications in solving analytic geometry problems and carrying out graphic symmetry transformation.
2. Let's define what point symmetry is. Let point A (x 1, y 1) and point B (x2, y2) be symmetrical about point A (b), then there is an equation: (x1+x2)/2 = a (y1+y2)/2.
3. From this, the coordinate formulas of the symmetrical points can be derived: x2=2a-x 1, y2=2b-y 1. This formula tells us how the coordinates of a point's symmetry point change relative to another point.
Function of mathematical symmetry point formula
1, symmetry point formula plays an important role in solving analytic geometry problems. In the plane rectangular coordinate system, for a given point A, we can find its symmetric point about another specific point B through the symmetric point formula. This is very useful for solving some geometric problems, such as finding the symmetrical figure of a figure or finding the symmetrical point of a point in a figure.
2. Symmetry point formula is also the basis of graphic symmetry transformation. In graphic design, art, architecture and other fields, it is often necessary to symmetrically transform graphics to create new graphics. Through the symmetry point formula, we can easily realize the symmetrical transformation of graphics, thus creating novel and interesting graphics.
3. Symmetry point formula can also help us better understand some concepts in algebra. For example, when studying group theory and linear algebra, we often need to study the properties of symmetric transformation and symmetric matrix. Through the symmetry point formula, we can better understand these concepts, so as to better grasp the knowledge in these mathematical fields.
4. Symmetry point formula can also help us solve some practical problems. For example, symmetry is a very important concept in physics. Through the symmetry point formula, we can better understand some phenomena in physics, such as mirror symmetry, rotational symmetry and so on.