Question

dilations: scale factor
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 } } )?
units

Explanation:

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

By counting the grid units, \( \overline{CD} = 3 \) units.

Step2: Use the dilation formula

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

Answer:

\( 12 \)