Eighth grade $\newline$ S. $11$ Checkpoint: Similarity transformations Drw $\newline$ Analytics $\newline$ Rectangle $A B C D$ is dilated by a scale factor of $2$ and translated $5$ units down. $\newline$ What is the perimeter of the image? $\newline$ units $\newline$ What is the area of the image? $\newline$ square units $\newline$ Submit $\newline$ Desk $1$

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Q. Eighth grade

\newline

11

Checkpoint: Similarity transformations Drw

\newline

Analytics

\newline

Rectangle

A B C D

is dilated by a scale factor of

2

and translated

5

units down.

\newline

What is the perimeter of the image?

\newline

units

\newline

What is the area of the image?

\newline

square units

\newline

Submit

\newline

Desk

1

Original Dimensions: First, we need to know the original dimensions of rectangle ABCD to calculate the perimeter and area of the image after the transformation. However, since the problem does not provide the original dimensions of rectangle ABCD, we will assume that the original rectangle has a length of ' $l$ ' units and a width of ' $w$ ' units.
Perimeter of Original Rectangle: The perimeter of the original rectangle ABCD is calculated by adding the lengths of all four sides. The formula for the perimeter $P$ of a rectangle is $P = 2l + 2w$ .
Dilation by Scale Factor of $2$ : When rectangle ABCD is dilated by a scale factor of $2$ , both the length and the width are multiplied by $2$ . The new length of the image will be $2l$ and the new width will be $2w$ .
New Perimeter of Dilated Image: The new perimeter of the dilated image will be $P' = 2(2l) + 2(2w) = 4l + 4w$ . This is twice the original perimeter since each dimension is doubled.
Area of Original Rectangle: The area of the original rectangle ABCD is calculated by multiplying the length by the width. The formula for the area $A$ of a rectangle is $A = lw$ .
Area After Dilation: When the rectangle is dilated by a scale factor of $2$ , the area of the image will be multiplied by the square of the scale factor. The new area will be $A' = (2l)(2w) = 4lw$ , which is four times the original area.
Translation Effect: The translation of the rectangle $5$ units down does not affect the perimeter or the area of the image. Therefore, the perimeter and area calculations remain the same after the translation.