Question

quadrilateral ( a ^ { prime } b ^ { prime } c ^ { prime } d ^ { prime } ) is the image of quadrilateral ( a b c d ) under a dilation with a scale factor of 3.
what is the length of segment ( overline { b c } )?
2 units

Explanation:

Step1: Determine the length of \( \overline{B'C'} \)

Count the units on the grid. \( \overline{B'C'} = 6 \) units.

Step2: Use the dilation formula

Since dilation scale factor \( k = 3 \), and \( B'C'=k\times BC \). So \( BC=\frac{B'C'}{k} \).
Substitute \( B'C' = 6 \) and \( k = 3 \): \( BC=\frac{6}{3}=2 \).

Answer:

\( 2 \) units