01
Derive the proposed translation
Subtract P’s source coordinates from its target: 4 minus 1 gives 3 in x, and 1 minus 2 gives negative 1 in y. The proposed rule is therefore add 3 to x and subtract 1 from y. Applying it to Q at (5,3) gives (8,2), which matches the supplied target. The two pairs are consistent with the same translation. They do not prove that translation is the right model for every possible point, so retain a third correspondence as an additional check rather than treating a neat first calculation as complete validation.
02
Check a point that does not fit
Let source R be (2,6), with supplied target (5,6). The proposed translation predicts (5,5), so the target differs by zero in x and one in y. Record that residual rather than silently changing the target to fit the rule. The mismatch could arise from a mistaken pairing, a transcription issue or a transformation more complex than a translation; the abstract exercise does not decide which. Its useful result is the visible inconsistency. A report should identify the point and both positions so someone can investigate the source information.
03
Preserve the mapping and its exception
Use columns for label, source pair, supplied target, predicted target and residual. P and Q have residual (0,0); R has residual (0,1), defined here as supplied target minus prediction. State that sign convention above the table. The inverse translation subtracts 3 from x and adds 1 to y, returning a predicted point to its source. Keep the exception row with the proposed mapping. That prevents a later reader from mistaking a partially consistent exercise for a fully accepted alignment or overlooking which correspondence still needs attention.