Question

unit 2 midunit test: scale factor & dilations
name: _________________________
date: ___________ class: _____
mcc.8.g.4

1. a rectangle has side lengths 6 cm and 9 cm. what would the side lengths of the image be after a dilation of 2.25? explain or show your reasoning.

image of a rectangle with 6 cm (height) and 9 cm (width)
(3 points - 2 for correct lengths and 1 for the work/explanation)
.8.g.3
identify the scale factor of each of the...

Explanation:

Step1: Recall dilation formula

To find the side lengths after dilation, we multiply each original side length by the scale factor. The formula for a side length \( s' \) after dilation with scale factor \( k \) is \( s' = s \times k \), where \( s \) is the original side length.

Step2: Calculate new length for 6 cm side

For the side with length 6 cm, multiply by the scale factor 2.25.
\( 6 \times 2.25 = 13.5 \) cm.

Step3: Calculate new length for 9 cm side

For the side with length 9 cm, multiply by the scale factor 2.25.
\( 9 \times 2.25 = 20.25 \) cm.

Answer:

After a dilation of 2.25, the side lengths of the rectangle will be 13.5 cm and 20.25 cm.