Question

part a (2 points):
a dilation with a center at p(0,0) and a scale factor k is applied
to segment mn.

let segment mn represent the image of segment mn after the
dilation.

select each correct statement.
(select all that apply.)
□ if k > 0, then mn > mn.
□ if k > 1, then mn > mn.
□ if 0 < k < 1, then mn < mn.
□ if 0.5 < k < 1.5, then mn < mn.
□ if k = 1, then mn = mn.
□ if k = 0.5, then mn = 0.5(mn).

part b (3 points):

Explanation:

Step1: Recall Dilation Property

Dilation with scale factor \( k \) (center at origin) transforms a segment \( MN \) to \( M'N' \) where \( M'N' = k \times MN \).

Step2: Analyze Each Statement

• Statement 1: \( k>0 \Rightarrow M'N'>MN \)

If \( k = 0.5 \) (which is \( >0 \)), \( M'N' = 0.5MN < MN \). So false.

• Statement 2: \( k>1 \Rightarrow M'N'>MN \)

If \( k>1 \), \( k \times MN > MN \) (since \( MN>0 \)). So true.

• Statement 3: \( 0

If \( 00 \)). So true.

• Statement 4: \( 0.5

If \( k = 1.2 \) (in \( 0.5 MN \). So false.

• Statement 5: \( k = 1 \Rightarrow M'N' = MN \)

If \( k = 1 \), \( M'N' = 1 \times MN = MN \). So true.

• Statement 6: \( k = 0.5 \Rightarrow M'N' = 0.5(MN) \)

By dilation formula, \( M'N' = 0.5 \times MN \). So true.

Answer:

B. If \( k > 1 \), then \( M'N' > MN \)
C. If \( 0 < k < 1 \), then \( M'N' < MN \)
E. If \( k = 1 \), then \( M'N' = MN \)
F. If \( k = 0.5 \), then \( M'N' = 0.5(MN) \)