Difficulty: Hard

Average Score: 37%

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 PQRS is 25 square units.

To find the area, we first recognize that the problem involves a quadrilateral with a specific transformation or size change, leading us to calculate the area based on the dimensions involved. Given the calculations leading to the answer, we arrive at an area of 25 square units for the image of PQRS.

A (20) YOUR ANSWER

This choice suggests an area smaller than the calculated value. The calculations leading to 25 square units indicate that the dimensions or transformations applied to PQRS resulted in a larger area, meaning that 20 square units does not reflect the correct transformation or scaling of the quadrilateral.

B (25) CORRECT

This is the correct answer, as it matches the calculated area resulting from the transformations applied to the quadrilateral PQRS. The steps provided in the question lead to this specific area, confirming that it accurately reflects the dimensions of the transformed shape.

C (40) YOUR ANSWER

Choosing 40 implies an area larger than the calculated value. The calculations show that the transformation does not yield an area of 40 square units. This discrepancy indicates an overestimation of the dimensions or an incorrect understanding of how the transformations affect the area of PQRS.

D (50) YOUR ANSWER

An area of 50 suggests a significant increase in size that does not align with the calculations leading to 25 square units. This choice indicates a misunderstanding of the scaling or transformation process applied to PQRS, resulting in an inflated area that is not supported by the calculations.

E (100) YOUR ANSWER

This option indicates a double area compared to the calculated value. Such a large area suggests an exaggerated transformation that is not reflected in the steps leading to 25 square units. This choice misrepresents the actual dimensions and scaling of the quadrilateral.

Conclusion

The area of the image of PQRS calculated through the provided steps is 25 square units. This value is derived from the transformations and dimensions applied to the quadrilateral. All other options reflect misunderstandings or incorrect calculations of the area based on the transformation or scaling factors involved. Thus, understanding the correct area is crucial for solving this type of geometric problem accurately.