Triangle xyz was transformed by a dilation with center O and scale factor $3$. If the original length of side xy was $1.5$ units, what is the length of side xy after the transformation?

• A. $4.5$
• B. $18$
• C. $3$
• D. $1.5$

Answer: (A)

Verified step by step guidance

1. Understand that a dilation transformation changes the size of a figure by a scale factor relative to a fixed point called the center of dilation.
2. Identify the given scale factor, which is 3, meaning every length in the figure will be multiplied by 3 after the dilation.
3. Note the original length of side xy, which is 1.5 units before the transformation.
4. Apply the dilation formula for lengths: \(\text{new length} = \text{original length} \times \text{scale factor}\).
5. Calculate the new length of side xy by multiplying 1.5 by 3, which gives the length of side xy after the transformation.