What you’ll learn
Understand translations.
Key idea
A translation adds the same signed horizontal and vertical changes to every point; congruence alone is insufficient.
A translation requires the same displacement for every corresponding point; congruence alone is insufficient.
Worked example
Classify examples and non-examples for the concept 'Understand translations'.
Points [(-2, -2), (0, -1)] have proposed images [(-3, -1), (0, 0)] in matching order. Classify whether this correspondence is a translation, with vector evidence.
- For a translation every point moves by the same vector (-1,1); actual image table is [((-2, -2), (-3, -1)), ((0, -1), (-1, 0))].
- Add the signed components separately: (-2+(-1),-2+(1))=(-3,-1); unequal displacements are not a translation.
Answer: No — not both displacements equal (-1,1); a translation requires one common vector.
Quick Check
Classify examples and non-examples for the concept 'Understand translations'.
Points [(-2, -1), (0, 0)] have proposed images [(-5, 1), (-3, 2)] in matching order. Classify whether this correspondence is a translation, with vector evidence.