Question

nalyzing the dilation of a rectangle
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: Calculate \(M'N'\)

Original \(MN = 6\). After dilation with scale factor \(3\), \(M'N'=6\times3 = 18\).

Step2: Determine dilation type

Since scale factor \(3> 1\), it is an enlargement.

Step3: Find scale factor

Given dilation rule \(D_{P,3}\), scale factor \(k = 3\).

Answer:

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