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: Recall the properties of dilation

Dilation formula: If a figure is dilated with a scale factor \(k\) from a center \(P\), then the length of each side of the dilated figure is \(k\) times the length of the corresponding side of the original figure. Here \(k = 3\) (from the rule \(D_{P,3}\)).

Step2: Calculate the length of \(M'N'\)

The length of \(MN\) is \(6\) units. Using the dilation formula \(M'N'=k\times MN\). Substitute \(k = 3\) and \(MN = 6\) into the formula: \(M'N'=3\times6=18\) units.

Step3: Determine if it is a reduction or enlargement

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

Answer:

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