Triangles Q R S and A B C are shown. The lengths of sides Q R and A B are 16 centimeters. The lengths of sides R S and B C are 24 centimeters. Angles Q R S and A B C are right angles. Sides Q S and A C are parallel and identical to each other and there is space in between the 2 triangles.

To determine whether there is a series of rigid transformations that can map triangle \( \Delta QRS \) to triangle \( \Delta ABC \), we first analyze the properties of the triangles given in the problem.

1. Both triangles are right triangles.
2. The lengths of the sides \( QR \) and \( AB \) are both 16 cm.
3. The lengths of the sides \( RS \) and \( BC \) are both 24 cm.
4. The sides \( QS \) and \( AC \) are parallel and identical, meaning they also have the same length.

Since both triangles have the same side lengths: \( QR = AB \), \( RS = BC \), and \( QS = AC\), they are congruent by the Side-Side-Side (SSS) congruence postulate.

Given that the triangles are congruent, we need to determine if a series of rigid transformations can map \( \Delta QRS \) to \( \Delta ABC \). Rigid transformations include translations, rotations, and reflections, which preserve distance and angles.

Let's analyze the options given in the problem:

1. No, \( \Delta QRS \) and \( \Delta ABC \) are congruent but \( \Delta QRS \) cannot be mapped to \( \Delta ABC \) using a series of rigid transformations.

   • This statement is incorrect since congruent triangles can always be mapped onto each other with rigid transformations.

2. No, \( \Delta QRS \) and \( \Delta ABC \) are not congruent.

   • This statement is also incorrect since we determined the triangles are congruent by SSS.

3. Yes, \( \Delta QRS \) can be translated so that \( R \) is mapped to \( B \) and then rotated so that \( S \) is mapped to ( C.

   • This option is plausible. A translation to align \( R \) with \( B \), followed by a rotation to place \( S \) on \( C \) could work assuming proper orientation is maintained.

4. Yes, \( \Delta QRS \) can be translated so that \( Q \) is mapped to \( A \) and then reflected across the line containing ( QS.

   • This option is also plausible. Translating \( Q \) to \( A \) and reflecting across the line containing \( QS \) could map \( \Delta QRS \) onto \( \Delta ABC\).

Given these considerations, both options 3 and 4 could accurately describe transformations that would map \( \Delta QRS \) to \( \Delta ABC \). However, since the prompt requires a single yes/no answer, the definitive conclusion is:

Yes, \( \Delta QRS \) can be translated so that \( R \) is mapped to \( B \) and then rotated so that \( S \) is mapped to ( C.