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 4.
what is the length of segment ( overline{c^{prime} d^{prime}} )?

Explanation:

Step1: Determine the length of segment \( \overline{CD} \)

By counting the grid units, the length of \( \overline{CD} \) is \( 3 \) units.

Step2: Apply the dilation formula

Since the scale factor \( k = 4 \), and the formula for the length of a dilated segment is \( L'=k\times L \). Substitute \( L = 3 \) and \( k = 4 \) into the formula: \( L'=4\times3 \).

Answer:

\( 12 \)