Question

a triangle is dilated by a scale factor of ( n = \frac{1}{3} ). which statement is true regarding the dilation?
it is an enlargement because ( n > 1 ).
it is a reduction because ( n > 1 ).
it is an enlargement because ( 0 > n > 1 ).
it is a reduction because ( 0 < n < 1 ).

Explanation:

Step1: Recall Dilation Rules

Dilation: If scale factor \( n > 1 \), it's enlargement; if \( 0 < n < 1 \), it's reduction.

Step2: Analyze Given Scale Factor

Given \( n=\frac{1}{3} \). Check \( n \)’s range: \( 0 < \frac{1}{3} < 1 \). So dilation is reduction (since \( 0 < n < 1 \)).

Answer:

It is a reduction because \( 0 < n < 1 \) (the fourth option: "It is a reduction because \( 0 < n < 1 \)")