Calculate the length of a straight line

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Regardless of whether you need to determine the distance between two points or calculate the length of a straight line between two points, the procedure is always the same.

Do not despair when calculating the length.
Do not despair when calculating the length.

Determine the length of a straight line between two points

In order to be able to calculate the length, you have to define the endpoints of a Straight lines know. If you have not given this, you have to calculate it beforehand. However, if you do not have any information about the position of the endpoints of a straight line, it is infinitely long.

  1. The distance between two points is identical to the length of the straight line that runs through the two points and is bounded by them. So, given two points, you can use Pythagorean theorem and a slope triangle to calculate the length.
  2. The Pythagorean theorem is generally: a2 + b2 = c2. A slope triangle is a right-angled triangle in which the legs a and b are determined by the difference in the position of the points P.1(x1/ y1) and P2(x2/ y2) can be calculated.
  3. You can calculate a as follows: a2 = (x1 - x2)2.
    Calculate the length of b with the y-values: b2 = (y1 - y2 )2.
  4. Substituting the values ​​in the Pythagorean Theorem, you get the square of the length of the straight line between the points P.1 and P2 as follows:
    c2 = (x1 - x2)2 + (y1 - y2 )2.
    5. Proportionality factor - this is how you determine it

    A function is proportional when it goes through the origin and has a positive ...

  5. Finally, pull the root and you will get the length you are looking for.

Calculating the length in three-dimensional space

The calculation of the length in three-dimensional space is mostly used in schools for vectors. However, the formula can also be used on straight lines between two points.

  1. First you have to find the three differences of the coordinates P1(x1/ y1/ z1) and P2(x2/ y2/ z2) to calculate. Use the following formulas for this:
    a2 = (x1 - x2)2
    b2 = (y1 - y2 )2
    c2 = (e.g.1 - e.g.2 )2.
  2. The square of the segment v between the two points P.1 and P2 can now be calculated by inserting the calculated values ​​into the following formula:
    v2 = a2+ b2 + c2.
  3. Now pull the root of v2 to get the segment or length v.

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