Question

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

Explanation:

Step1: Understand reflection and translation

Reflection flips a figure over a line. Translation slides a figure without rotating or resizing.

Step2: Analyze the first pair

For the first pair of triangles (with points \(Q, A, R, L, K\)), we can first reflect one triangle over the line \(QR\) (or \(LK\) - since \(QR = LK\) as marked by the equal - length symbol) and then translate it. The right - angle and the side - length relationships (marked by the equal - length symbol) suggest that after reflection (which changes the orientation in a mirror - like way) and translation (sliding), one triangle can be mapped to the other.

Step3: Analyze the second pair

For the second pair (with points \(L, P, K, Q, R, A\)), the orientation of the right - angles and the side - length relationships (if we assume the vertical sides \(KP\) and \(QR\) are not equal in a way that would allow a simple reflection - translation mapping) do not support a mapping using only reflection and translation.

Answer:

The first pair of triangles (the one with points \(Q, A, R, L, K\)) can be mapped to each other using a reflection and a translation.