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.
(diagram: rectangle lmnp (larger, blue) with lm = 12; smaller rectangle lmnp (blue) with lm = 4, mn = 6; points l, m, n, p and l, m, n, p labeled.)

Explanation:

Step1: Analyze scale factor

The dilation rule is \( D_{P,3} \), so scale factor \( k = 3 \). Original \( MN = 6 \), so \( M'N' = 6\times3 = 18 \).

Step2: Determine dilation type

Since \( k = 3>1 \), it's an enlargement.

Step3: Evaluate each statement

• "The length of line segment \( M'N' \) is 18 units." True (from Step1).
• "The length of segment \( M'N' \) is 14 units." False (calculated 18).
• "The dilation is a reduction." False (\( k>1 \), enlargement).
• "The dilation is an enlargement." True (\( k = 3>1 \)).
• "The scale factor is \( \frac{1}{3} \)." False (scale factor is 3).
• "The scale factor is 3." True (from dilation rule).

Answer:

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