Question

Which of these triangle pairs can be mapped to each other using a reflection and a translation?

Triangles L R K and A R Q are connected at point R. Triangle L R K is reflected across point R to form triangle A R Q.
Triangles L P K and Q R A are shown. Triangle L P K is reflected across a line to form triangle Q R A. Triangle Q R A is shifted to the right of triangle L P K.
Triangles L P K and Q R A are shown. Triangle L P K is shifted down and to the left to form triangle Q R A.
Triangles L P K and Q R A are shown. Triangle L P K is rotated to form triangle Q R A. Triangle Q R A is also shifted to the right.

Answer 1

Only the second pair.

Reasoning:
- Pair 2: explicitly produced by a reflection across a line and then a translation (reflection + shift) — so it matches.
- Pair 1: is a point reflection (180° rotation about R), which is an orientation-preserving half-turn and cannot be obtained by a single line-reflection plus a translation.
- Pair 3: is just a translation (no reflection used), so it does not require a reflection+translation.
- Pair 4: uses a rotation (and a shift), not a reflection, so it cannot be realized by a reflection plus a translation.