Question

rectangle lmnp was dilated using the rule ( d_{p,3} ). which statements are true? check all that apply.

the length of line segment ( mn ) is 18 units.

the length of segment ( mn ) is 14 units.

the dilation is a reduction.

the dilation is an enlargement.

the scale factor is ( \frac{1}{3} ).

the scale factor is 3.

Explanation:

Step1: Determine the scale factor

The dilation rule is \(D_{P,3}\), so the scale factor \(k = 3\).

Step2: Analyze the type of dilation

Since \(k=3> 1\), the dilation is an enlargement.

Step3: Calculate the length of \(M'N'\)

The original length \(MN = 6\). After dilation, \(M'N'=k\times MN\). Substitute \(k = 3\) and \(MN = 6\), we get \(M'N'=3\times6 = 18\).

Answer:

• The length of line segment \(M'N'\) is 18 units.
• The dilation is an enlargement.
• The scale factor is 3.