Triangle xyz is dilated by a scale factor of $3$ centered at the origin. If the original length of side $xy$ is $5$ units, what is the length of side $xy$ after the transformation?

• A. $15$ units
• B. $3$ units
• C. $5$ units
• D. $8$ units

Answer: (A)

Verified step by step guidance

1. Understand that a dilation centered at the origin with a scale factor k multiplies all lengths in the figure by k.
2. Identify the given scale factor k = 3 and the original length of side xy = 5 units.
3. Apply the dilation formula for lengths: New length = Scale factor \(\times\) Original length.
4. Substitute the known values into the formula: New length = 3 \(\times\) 5.
5. Express the new length of side xy after dilation as 15 units (without calculating the final numeric value here).