Algebra!
How is the distance formula and the pythagorean theroem similar?
The distance formula follows from the pythagorean theorem. You have to apply it twice:
If (x1, y1, z1) are the coordinates of a point 1 and (x2, y2, z2) are the coordinates of point 2, then the distance S is given by:
S^2 = (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2
If you project everything on the x-y plane then the distance is obviously given by Pythagoras' theorem. The square of the distance is the sum of the first two terms. Applying this theorem again, you see that you have to add to this the squared distance in the z-direction to find the square of the total distance.
According to the theroy of special relativity the distance between two points is not the same for all observers. You have to include the time coordinate as well to get an "invarian"distance formula:
S^2 = (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2
- c^2 (t1 - t2)^2
where c is the speed of light
This function is the same for all observers.
how i can find coordinate of each point.
To find the coordinates of each point, you will need to know the specific information or context given in the problem or situation. Here are a few examples of how you can find the coordinates of points in different scenarios:
1. Cartesian Coordinate System: In a two-dimensional Cartesian coordinate system, points are represented by their x and y coordinates. To find the coordinates of a point, you need to know its position along the x-axis and y-axis. For example, if a point is located 3 units to the right and 2 units above the origin, its coordinates would be (3, 2).
2. Three-Dimensional Coordinate System: In a three-dimensional Cartesian coordinate system, points are represented by their x, y, and z coordinates. Similar to the previous example, you need to know the position of the point along each of the three axes. For instance, if a point is located 1 unit to the left, 2 units in front, and 4 units above the origin, its coordinates would be (-1, 2, 4).
3. Geographic Coordinates: In geography, points on the Earth's surface are often represented using latitude and longitude coordinates. Latitude specifies the point's position north or south of the equator, while longitude specifies its position east or west of the Prime Meridian. To find the coordinates of a specific location on the Earth, you can use maps, GPS devices, or online tools.
4. Other Coordinate Systems: Depending on the problem or application, there may be other coordinate systems to consider. Examples include polar coordinates, cylindrical coordinates, and spherical coordinates. Each system has its own unique way of representing points, and you would need to know the appropriate formulas or conversion methods specific to that system.
In summary, finding the coordinates of points depends on the coordinate system being used and the information provided in the problem or situation.