Question

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

Explanation:

Step1: Recall reflection and translation properties

Reflection flips a figure over a line and translation slides it. For two triangles to be mapped to each other using these, they must be congruent and have the right orientation - after reflection, translation can align them.

Step2: Analyze triangle pairs visually

Check each pair. Look for a pair where one triangle can be flipped (reflected) to match the orientation of the other and then moved (translated) to exactly overlap. In the first - type of pair shown (top - most in the image), if we reflect one triangle over an appropriate line (e.g., a vertical line between them) and then translate it horizontally and vertically, it can match the other triangle. In the second - type of pair (bottom - most in the image), no combination of reflection and translation can make them coincide as their relative orientations are not correct for such a mapping.

Answer:

The top - most triangle pair (the pair with triangles QRA and LKR) can be mapped to each other using a reflection and a translation.