Question

activity 4.4.1 - dilations

1. rectangle a is dilated to form rectangle b

image of rectangle a (length 4, width 6) and rectangle b (length 20, width 30)

what scale factor was used? enter the answer and also provide a 1 sentence explanation that describes how you determined your answer.

Explanation:

Step1: Recall scale factor formula

The scale factor \( k \) for dilation is given by \( k=\frac{\text{Length of image}}{\text{Length of original}} \).

Step2: Apply to length

For the length, original (rectangle A) has length 4, image (rectangle B) has length 20. So \( k = \frac{20}{4}=5 \).

Step3: Verify with width

Original width is 6, image width is 30. \( \frac{30}{6}=5 \), which matches.

Answer:

The scale factor is 5, determined by dividing the length (or width) of rectangle B by the corresponding length (or width) of rectangle A.