Question

circle e and diameter \\( \overline { d f } \\) are shown on the graph below. circle e is dilated by a scale factor of 5 centered at \\( ( 5,1 ) \\) to create circle \\( e ^ { prime } \\).

what is the circumference of circle \\( e ^ { prime } \\)?

write your answer as a whole number or as a decimal rounded to the nearest tenth.

units

Explanation:

Step1: Find the diameter of circle \( E \)

From the graph, the diameter \( DF \) of circle \( E \) is \( 4 \) units (count the grid - squares between \( D \) and \( F \)).

Step2: Find the diameter of circle \( E' \)

Since the circle \( E \) is dilated by a scale factor of \( 5 \), the diameter of circle \( E' \), \( d'=4\times5 = 20 \) units.

Step3: Calculate the circumference of circle \( E' \)

The formula for the circumference of a circle is \( C=\pi d \). Substitute \( d = 20 \) into the formula: \( C=\pi\times20\approx3.14\times20 = 62.8 \) units.

Answer:

\( 62.8 \)