Question

Rectangle P′R′S′T′ is a dilation of rectangle PRST with a scale factor of 3. Write an equation for the area of P′Q′R′S′ if the sides of the original rectangle PQRS were x and y.

A) 3xy
B) 9xy
C) (x/3) * (y/3)
D) xy

Answer 1

The area of the dilated rectangle P'Q'R'S' is 9xy because the rectangle was dilated with a scale factor of 3, which when squared gives us the new area (3^2 * xy = 9xy).

Step-by-step explanation:

The question is asking for the area of a dilated rectangle compared to the original rectangle with sides x and y. When a rectangle is dilated with a scale factor of 3, its length and width are both multiplied by the scale factor. The area of the original rectangle is x times y (xy).

By the properties of dilation, to find the new area after dilation, we multiply the original area by the square of the scale factor (because area is a two-dimensional measure). Here, the scale factor is 3, so the new area will be (3)^2 times the original area (3^2 * xy = 9xy). Therefore, the correct answer is B) 9xy.