Square PQRS, with a side length of 5 units, will be translated 2 units to the right and 2 units up in the standard (x, y) coordinate plane. What is the area, in square units, of the image of PQRS?

Rationale

The area of the image of square PQRS is 25 square units.

The area of a square is calculated using the formula A = side length × side length. Since square PQRS has a side length of 5 units, the area remains constant at 25 square units after translation, as translations do not alter the size of geometric figures.

A (20) YOUR ANSWER

This choice incorrectly suggests that the area of the square decreases to 20 square units. However, translations do not change the area of geometric shapes; they only change their position. Therefore, the area remains 25 square units.

B (25) CORRECT

This is the correct answer, as the area of square PQRS is calculated by squaring its side length: 5 units × 5 units = 25 square units. The translation of the square does not affect its area.

C (40) YOUR ANSWER

This option implies an incorrect increase in the area of the square to 40 square units. The area of a square depends solely on its side length, which has not changed, so the area remains 25 square units regardless of any translations.

D (50) YOUR ANSWER

Choosing 50 suggests that the area has doubled, which is incorrect. The area of a square cannot change due to translation; it is solely dependent on the side length, which remains at 5 units, resulting in an area of 25 square units.

E (100) YOUR ANSWER

This choice significantly overestimates the area, suggesting a size increase to 100 square units. This is impossible since the area is determined by the side length of 5 units. Thus, the area remains 25 square units.

Conclusion

The area of square PQRS, which has a fixed side length of 5 units, is calculated to be 25 square units. Translations of geometric figures do not alter their sizes or areas, confirming that the area of the translated image of PQRS remains at 25 square units.