Question

quadrilateral ( abcd ) is the image of quadrilateral ( abcd ) under a dilation with a scale factor of 3. what is the length of segment ( overline{bc} )? units

Explanation:

Step1: Count the length of \( B'C' \)

By counting the grid - squares, \( B'C'=6 \) units.

Step2: Use the dilation formula

Since the scale factor \( k = 3 \) and \( B'C'=k\times BC \). Let \( BC=x \), then \( 6 = 3x \).

Step3: Solve for \( x \)

Divide both sides of the equation \( 6 = 3x \) by 3. We get \( x=\frac{6}{3}=2 \).

Answer:

\( 2 \)