Question

preimage
image
scale factor = 5
4
12
what is the area of the image?
1,500 u²
1,200 u²
1,860 u²
48 u²
re you continue, we recommend completing the day 2 activity,
am design*

Explanation:

Step1: Find scaled dimensions

The preimage is a rectangle with length \( 12 \) and width \( 4 \). The scale factor is \( 5 \), so the scaled length is \( 12\times5 = 60 \) and the scaled width is \( 4\times5 = 20 \).

Step2: Calculate image area

The area of a rectangle is \( \text{length}\times\text{width} \). So the area of the image is \( 60\times20 = 1200 \, \text{u}^2 \)? Wait, no, wait: Wait, \( 12\times5 = 60 \), \( 4\times5 = 20 \), then \( 60\times20 = 1200 \)? Wait, no, wait, \( 12\times4 = 48 \) (preimage area), and when scaling by factor \( k \), area scales by \( k^2 \). So preimage area is \( 12\times4 = 48 \), scale factor squared is \( 5^2 = 25 \), so image area is \( 48\times25 = 1200 \)? Wait, no, \( 48\times25 = 1200 \)? Wait, \( 48\times20 = 960 \), \( 48\times5 = 240 \), \( 960 + 240 = 1200 \). Yes.

Answer:

\( 1200 \, \text{u}^2 \) (corresponding to the option "1,200 u²")