How do you find a point so that it is the shortest sum of distances from each point?

is a point on a straight line.

If there are n points in the order, the coordinates are (an,0), and the points are all in the x-axis upward.

Again, let the coordinates of the shortest point be (am,0),m=(n+1) 2

When m is a fraction, its range is the integer part of m, set to t, and the coordinates of the shortest point should be between [at,at+1].

A straight line is made up of an infinite number of points. Straight lines are the constituent parts of a surface and in turn make up the body. There are no endpoints, and the length is inmeasurable and extends indefinitely to both ends. A straight line is an axisymmetric figure.

It has an infinite number of axes of symmetry, one of which is itself, and all the straight lines (with an infinite number of axes) perpendicular to it. If there is only one straight line at two points that do not coincide on the plane, that is, two points that do not coincide determine a straight line. On a spherical surface, crossing two points can make an infinite number of similar straight lines.

The most basic elements that make up a geometry. In the axiomatic system of Euclidean geometry established by D. Hilbert, points, lines, and planes are basic concepts, which are defined by their relations and five sets of axioms.

,.. a1, a2An is sorted by coordinate size to get p1, p2 ,..pn If n is an odd number, take b=p((n+1) 2), that is, if the middle point is an even number, take b as any point on the line segment p(n 2)p(n 2+1).

The reason is very simple, remember f(x)=sum(abs(an-x)), when x is on the right side (i.e., at the middle point or on the right side of the segment), f is a positive (continuous) polyline segment with a slope, and when x is on the left, f is a polyline segment with a negative slope, and the minimum value can be judged according to monotonicity.

In a two-dimensional coordinate system, the distance between two points can be calculated using the distance formula. Suppose there are two points a(x1, y1) and b(x2, y2) and the distance d between them can be calculated using the following formula:

d = x2 - x1)^2 + y2 - y1)^2)

where x1, y1) is the coordinate of point a, and x2, y2) is the coordinate of point b, which represents the square root and calculates the straight-line distance between two points.

This distance formula is derived from the Pythagorean theorem, which can be used to calculate the distance between any two points, and is only applicable to two-dimensional coordinate systems, as well as to higher-dimensional coordinate systems.

It is important to note that this distance formula only works for straight-line distances, which are the shortest distance between two points. If you want to calculate other types of distances between two points, such as curve distances or path lengths, you need to use different methods to calculate them according to the specific situation.

The distance d between one point (x,y) and three points (x1,y1), (x2,y2) and (x3,y3) is.

d=sqrt((x-x1)^2+(y-y1)^2)+sqrt((x-x2)^2+(y-y2)^2)+sqrt((x-x3)^2+(y-y3)^2)

Find min d, so that dd infiltration front dx=0, dd dy=0, find x and cong touch y, and enter the above equation on behalf of noisy chang.

In ancient times, two merchants got lost while passing through a desert.

The desert is vast and boundless, and there is no reference for a hundred miles, except for sand and sand.

They didn't know which way to go, and after walking for a while they walked back to where they were. At night, both of them were so stupid that they didn't even know how to look at the North Star, so they had to freeze in the desert for the night.

The next day, the two men had a disagreement. The first person insisted that he should go west, and the second person, although he did not know which way to go, did not agree with the first person's opinion, and said that this was the direction when he came, so how could he go back?

The conflict was not resolved, and the two men had to go their separate ways.

The first person thinks that no matter how far back or somewhere else, it is good to get out of the desert. So he was firm in his belief and went in only one direction. Although it is not a straight line to go in this direction.

After two days and two nights, he had run out of food and water. Just as he was in despair, he saw smoke rising not far in front of him, like a trouser to welcome him. In this way, the first man managed to get out of the desert.

The second person believes that the shortest distance between two points is a straight line, and as long as you take a straight line and do not take detours, you will definitely get out of the desert, and you will get out of the desert before the first person. To get out of the desert, he made a mark in place and headed east. After walking for a short time, he felt that something was wrong, thought that he had taken a detour, and returned to the same place.

Then I went south, and after a short time I turned back again. Then I walked north, and after walking for a long time, I still didn't see a single figure, thinking that I had gone wrong again, but I still returned to the same place. Next, he tried the southwest, northwest, southeast, and northeast, and tried Zheng Su in every direction, but he still returned to the same place.

By this time, he had run out of food and water. A few days later, not only did the man not get out of the desert before the first person, but he died in the desert. When he died, he still did not understand that there were no straight lines in the desert, only directions.

If you don't change your thinking and blindly pursue the so-called straight line, then what awaits you is only a dead end.

The third sentence is that the shortest distance between two points is not necessarily a straight line.

In the process of interpersonal relationships and doing things, it is difficult for us to get things done straightforwardly. Sometimes we need to wait, sometimes we need to cooperate, sometimes we need skill. We will encounter a lot of difficulties and obstacles in doing things, sometimes we don't have to be stiff and hard, we can choose to have difficulties to bypass, there are obstacles to bypass, maybe this will do things more smoothly.

Think about it, we have to think about which sentence is better when we talk to others. Especially in China's more complex society, you have to learn to find a way to understand others, and you have to make people feel that you are a mature and good person, so that you can get things done.

Note: If you are taking a math test, you must answer the shortest straight line between the two points, if you are walking, from A to B, you can go directly to it, but everyone does not walk, you better not walk, because there are traps. In doing things in China, linear thinking has to hit a wall in many places, which is the wisdom of Chinese characteristics.

The shortest between two points is not necessarily a straight line, because the page is not necessarily flat and the world is not necessarily a world.

We must have skill in doing things, we must have wisdom and vain, and there is no hope for brute force. Efforts that have been thoroughly thought out are effective efforts, otherwise many times, even if a lot of effort is spent, it will only be in vain.

This, self-remembered.

The distance between two points can be found using the formula:

Let the two points A and B and the coordinates (x1, y1) and (x2, y2) respectively, then the distance between points A and B is:

If it is a three-dimensional coordinate, let the two points A and B and the coordinates (X1, Y1, Z1) and (X2, Y2, Z2) respectively, then the distance between A and B is:

The distance formula between two points is often used in the function graph to find the distance between two points and the coordinates of the point, and the basic formula is slippery and is one of the distance formulas. The distance between two points is a statement that describes the relationship between points and the distances between points.

4 points are divided into two groups, 2 points are connected, and then the vertical line is made, and the intersection of the two vertical lines is the point sought.

The intersection of the diagonal lines of the 4 points is the point p.

Prove it yourself when you have time.