????Math Question????8th grade adv.math

posted by Alex

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.

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