Of all the line segments connecting a point outside the straight line with a point on the straight line, the vertical line segment is the shortest, and the length of this vertical line segment is called the distance from the point to the straight line. Line Ax+By+C=0 coordinates (Xo, Yo) Then the distance from this point to this line is: │AXo+BYo+C│/√(A? +B？ )。

The length of the vertical section from a point outside a line to this line is called the distance from this point to this line. The distance of this vertical line segment is the shortest distance from any point to a straight line. Line Ax+By+C=0 coordinates (Xo, Yo) Then the distance from this point to this line is: │AXo+BYo+C│/√(A? +B？ )。

Of all the line segments connecting the outer point and the point on the line, the vertical line segment is the shortest.

The distance from a point to a straight line is called a vertical line segment.

Extended data

1. The combination of numbers and shapes is a common way of thinking to solve mathematical problems. The combination of numbers and shapes can make some abstract mathematical problems intuitive and vivid, change abstract thinking into image thinking, and help to grasp the essence of mathematical problems. In addition, due to the combination of numbers and shapes, many problems are easy to solve and the solutions are simple.

2. The so-called combination of numbers and shapes is the idea of solving mathematical problems through the mutual transformation of numbers and shapes according to the corresponding relationship between numbers and shapes, and the realization of the combination of numbers and shapes is often related to the following contents:

(1) The correspondence between real numbers and points on the number axis.

(2) The correspondence between function and image.

(3) The corresponding relationship between curve and equation.

(4) Concepts based on geometric elements and geometric conditions, such as complex numbers and trigonometric functions.

(5) The structure of a given equation or algebraic expression has obvious geometric significance. Such as equation.

3. Looking at the college entrance examination questions for many years, skillfully using the thinking method of combining numbers and shapes to solve some abstract mathematical problems can get twice the result with half the effort. The key point of the combination of number and shape is to study "helping number with shape"

4. The thinking method of combining numbers and shapes is widely used. For example, in solving equations and inequalities, in finding the range and maximum value of functions, in finding complex numbers and trigonometric functions, we can not only find the solution intuitively, but also avoid complicated calculation and reasoning, which greatly simplifies the problem-solving process.

This is more advantageous in solving multiple-choice questions and fill-in-the-blank questions. We should pay attention to cultivating this kind of ideology and try to have a picture in our mind to broaden our thinking horizons.

5. Number-shape combination theory.

In short, the idea of combining numbers and shapes is a mathematical idea of combining numbers and shapes to solve mathematical problems in mathematics. The combination of numbers and shapes is to combine abstract mathematical language with intuitive graphics, to combine abstract thinking with image thinking, and to solve mathematical problems through the correspondence and transformation of numbers and shapes.

There are three main types of solving math problems in middle schools: changing number into shape, changing number into shape, changing number into shape and changing number into shape.

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