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Not all datums are at right angles to other datums.  For example, looking at your street map (Figure 9), you see that the Museum is located on a street that's neither parallel nor at right angles to the streets the Hotel, Restaurant and Train Station are on.  Thus to determine how far it is from the Hotel to the Museum, you have to first translate your key origin to the Hotel and then rotate the key to be parallel to the street on which the Museum is located.  Now you can easily measure the distance from the Museum to the Hotel.

The exact same procedure applies to the workpiece (Figure 10).  The distance between the two holes on the workpiece can be measured once the original origin is translated to the smaller hole and the part coordinate system is mathematically rotated 45°.  Now both of the holes lie along the new Y axis and the distance can be calculated automatically.