01
Add compatible displacements
Write the first displacement as d1 = (3, 4) metres and the second as d2 = (−1, 2) metres, with east first and north second. Their sum is (2, 6) metres. The negative first component of d2 means west, so it reduces the eastward total from three to two. The northward components add from four and two to six. This component calculation is valid because both records describe displacements in the same frame and use the same units and ordering. Drawing the second arrow from the first arrow’s endpoint gives the same final displacement.
02
Reject a mismatched quantity
Now consider a record (3, 4) measured in metres per second. It describes a velocity rather than a displacement. Adding it directly to d1 would mix incompatible units, even though both records contain two numbers. The worksheet should flag the mismatch and leave the proposed sum unresolved. This is a dimensional distinction, not a judgement that one record is bad data. A separate model involving elapsed time could relate velocity to displacement, but that would introduce information and assumptions absent from this exercise.
03
Convert units before comparing records
A displacement recorded as (100, 200) centimetres becomes (1, 2) metres after dividing each component by one hundred. Only then can it be added to d1 to obtain (4, 6) metres. Keep the original values and the conversion in separate fields so a reviewer can reconstruct the calculation. A reusable record contains identifier, quantity type, axes, units, values and any conversion applied. If the frame differs as well as the units, a unit conversion alone is not enough to make the coordinate records compatible.