Question

line segment st is dilated to create line segment st using the dilation rule ( d_{q,2.25} ). what is x, the distance between points s and s?
options:
( x = 2.25 ) units
( x = 2.5 ) units
( x = 4.25 ) units
( x = 4.5 ) units

Explanation:

Step1: Recall Dilation Rule

Dilation with center \( Q \) and scale factor \( 2.25 \) means \( QS' = 2.25 \times QS \).

Step2: Calculate \( QS' \)

Given \( QS = 2 \), so \( QS' = 2.25 \times 2 = 4.5 \).

Step3: Find \( x \)

\( x = QS' - QS = 4.5 - 2 = 2.5 \).

Answer:

\( x = 2.5 \) units (Option: \( x = 2.5 \) units)