A parallelogram in a coordinate plane is reffected over the line \( y=5 \) and translated 2 units left and 1 unit down. Which statement is true? The resulting parallelogram is congruent to the original parallelogram only if the translation occurs first. The resulting parallelogram is congruent to the original parallelogran only if the reflection occurs first. The resulting parallelogram is not congruent to the original parallelogrann regardless of the order of the transformations. The resulting parallelogram is congruent to the original parallelogram regardless of the order of the transtormations.

To determine the correct statement regarding the transformations of the parallelogram, we need to analyze the effects of reflection and translation on the shape. 1. **Reflection over the line \( y = 5 \)**: - Reflecting a shape over a line preserves its size and shape. Therefore, the resulting shape after reflection will be congruent to the original shape. 2. **Translation (2 units left and 1 unit down)**: - Translating a shape also preserves its size and shape. Thus, the resulting shape after translation will also be congruent to the original shape. Now, let's consider the order of the transformations: - **If the reflection occurs first**: - The parallelogram is reflected over the line \( y = 5 \), resulting in a new parallelogram that is congruent to the original. - Then, translating this new parallelogram 2 units left and 1 unit down will still result in a shape that is congruent to the original parallelogram. - **If the translation occurs first**: - The parallelogram is translated 2 units left and 1 unit down, resulting in a new parallelogram that is congruent to the original. - Then, reflecting this new parallelogram over the line \( y = 5 \) will also yield a shape that is congruent to the original parallelogram. Since both transformations (reflection and translation) preserve congruence, the resulting parallelogram will be congruent to the original parallelogram regardless of the order in which the transformations are applied. Thus, the correct statement is: **The resulting parallelogram is congruent to the original parallelogram regardless of the order of the transformations.**