Question

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

Triangles Q R A and K P A are connected at point A. Triangle K P A is rotated to form triangle Q R A.
Triangles Q R A and K P L are shown. Triangle Q R A is reflected and then shifted to the right to form triangle K P L.
Triangles Q R A and K P L are shown. Triangle Q R A is reflected and then shifted to the right to form triangle K P L.
Triangles Q R A and K P L are shown. Triangle Q R A is rotated about point A and then is shifted down and to the left to form triangle K P L.

Answer 1

The 1st and the 4th pairs only.

- Pair 1 (QRA and KPA): KPA can be rotated about A to land on QRA, so a rotation about A (no translation needed) works.
- Pair 4 (QRA and KPL): it is obtained by a rotation about A followed by a translation — exactly the allowed moves.

Pairs 2 and 3 use a reflection (a flip), which changes orientation and cannot be produced by any combination of rotations and translations.