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}} )? units

Explanation:

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

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

Step2: Use the scale factor formula

The formula for dilation is \( \text{Length of image}=\text{Scale factor}\times\text{Length of pre - image}\). Given scale factor \( k = 4 \) and length of \( \overline{CD}=3 \) units. Then \( \text{Length of }\overline{C'D'}=k\times\text{Length of }\overline{CD}\).
Substitute \( k = 4 \) and \( \text{Length of }\overline{CD}=3 \) into the formula: \( \text{Length of }\overline{C'D'}=4\times3\).

Answer:

\( 12 \)