42. 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?
Answer: B
The area of the image of square PQRS after translation is 25 square units.
The area of a square remains unchanged regardless of its position on the coordinate plane. Since square PQRS has a side length of 5 units, its area is calculated as side length squared, which is 5 x 5 = 25 square units.
A) 20
This option is incorrect because it suggests an area smaller than that of the original square. The area of a square is determined by squaring its side length, which in this case is 5 units, leading to an area of 25 square units.
B) 25
This option is correct as it reflects the true area of square PQRS. The area is calculated by squaring the side length (5 units), yielding an area of 25 square units, which remains unchanged after translation.
C) 40
This option is incorrect because it implies an area greater than that of the original square. The area of a square cannot increase through translation alone, and the correct area is 25 square units.
D) 50
This option is incorrect as it suggests an area that is significantly larger than the actual area of the square. The area of square PQRS is determined by its side length and remains at 25 square units regardless of its position in the coordinate plane.
E) 100
This option is incorrect because it indicates an area that is four times larger than the actual area of the square. The area remains 25 square units regardless of translations.
Conclusion
The correct answer is option B, as the area of square PQRS is consistently 25 square units, arising from the side length of 5 units squared. All other options fail to represent the unchanged area of the square following its translation.