Finding Distances

1) Find the sides (Subtract the coordinates , locations or ruler markings to find the length of each side. Length is always positive.)

2) Square the sides (Multiply the length of each side by itself. Hint: be careful not to square the coordinates in step 1.)

3) Add or Subtract (Add the squares of the sides if the hypotenuse, diagonal or distance between points is unknown - this is the longest distance. Subtract the squares of the hypotenuse and of a side (leg) if the hypotenuse is known - any other side or distance must be shorter.)

4) Take the square root of the sum or difference. The result (distance) is always positive. See the explanation on Square Root


Note: This technique will work with any number of dimensions.

Examples:

           .
          /|              5        12        25               1  3   (Answer)
         / |             x5       x12      +144          _  ,------
    c=? /  |            ----     -----     -----       1  \/  1'69.
       /   | b=12        25       144       169       +1     -1
      /    |                                          ---    ------
     /     |                                           23    )  69
    '------'                                            -      -69
      a=5                                                      ====



           .
          /|            105         63       11025                8  4
         / |           x105        x63       -3369          _  ,-------
  c=105 /  |           -----       ----      ------       8  \/  70'56.
       /   | b=?        525        189        7056       +8     -64
      /    |          1050        378                    ---    -------
     /     |         -------     ------                  164      6 56
    '------'          11025       3969                   + 4     -6 56
      a=63                                                 -     ======



         ----------.
        /:        /|
       / :       / |
      /  :      /  |
     .---------.   | H=4
     |   :     |   |
     |   :.....|...|
     |  /      |  /
     | /       | / W=5
     |/        |/
     '---------'
        L=3




         ----------.
        /:        /|
   D=8 / :       / |
      /  :      /  |
     .---------.   | H=?
     |   :     |   |
     |   :.....|...|
     |  /      |  /
     | /       | / W=6
     |/        |/
     '---------'
        L=6

Last updated 6/2/97 - 5/8/2000.