Question

dilations: scale factor
google classroom microsoft teams
pentagon ( a ^ { prime } b ^ { prime } c ^ { prime } d ^ { prime } e ^ { prime } ) is the
image of pentagon ( a b c d e )
under a dilation with a scale factor
of ( \frac { 3 } { 2 } ).
what is the length of segment
( overline { a ^ { prime } b ^ { prime } } ) ?
units

Explanation:

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

From the grid, segment \( \overline{AB} \) has a length of \( 4 \) units.

Step2: Use the scale - factor formula

The formula for dilation is \( \text{Length of image segment}=\text{Scale factor}\times\text{Length of original segment} \).
Given scale factor \( k = \frac{3}{2} \) and length of \( \overline{AB}=4 \) units.
So, length of \( \overline{A'B'}=k\times\overline{AB}=\frac{3}{2}\times4 \).
Calculate \( \frac{3}{2}\times4 = 3\times2=6 \)

Answer:

\( 6 \)