Question

multiple choice 1 point a dilation with center o maps point b to b. what is the scale factor of this dilation? 1.1 ft (between o and b), 5.5 ft (between o and b)

Explanation:

Step1: Recall dilation scale factor formula

The scale factor \( k \) of a dilation with center \( O \) is the ratio of the distance from \( O \) to the image (\( OB' \)) to the distance from \( O \) to the original point (\( OB \)).

Step2: Identify distances

From the diagram, \( OB = 1.1 \) ft and \( OB' = 5.5 \) ft.

Step3: Calculate scale factor

Compute \( k=\frac{OB'}{OB}=\frac{5.5}{1.1} \). Simplifying, \( \frac{5.5}{1.1} = 5 \).

Answer:

The scale factor of the dilation is \( 5 \).