Question

practice 7 (from unit 3, lesson 3)
the triangle abc is taken to triangle abc by a dilation. select all of the scale factors for the dilation that would result in an image that was smaller than the original figure.
a $\frac{1}{2}$
b $\frac{5}{9}$
c 1
d $\frac{3}{2}$
e 2

Explanation:

Step1: Recall the property of dilation scale factor

A dilation with a scale factor \(k\) transforms a figure. If \(0 < k< 1\), the image is smaller than the original figure. If \(k = 1\), the image is congruent to the original figure. If \(k>1\), the image is larger than the original figure.

Step2: Analyze each option

• For option A: \(\frac{1}{2}=0.5\), and \(0 < 0.5<1\).
• For option B: \(\frac{5}{9}\approx0.56\), and \(0 < 0.56<1\).
• For option C: \(k = 1\), the image is congruent to the original.
• For option D: \(\frac{3}{2}=1.5\), and \(1.5>1\).
• For option E: \(k = 2\), and \(2>1\).

Answer:

A. \(\frac{1}{2}\), B. \(\frac{5}{9}\)