Questions: Which scale factor(s) will produce an image that is larger than the original? I. 0.86 II. 116% III. 8/5 I only I and II only II and III only I, II, and III

Which scale factor(s) will produce an image that is larger than the original? I. 0.86 II. 116% III. 8/5 I only I and II only II and III only I, II, and III

Solution

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Solution Steps

Step 1: Understand the Problem

We need to determine which scale factors will produce an image larger than the original. A scale factor greater than 1 will enlarge the image, while a scale factor less than 1 will reduce it.

Step 2: Analyze Each Scale Factor

  • Scale Factor I: 0.86

    The scale factor 0.86 is less than 1, which means it will reduce the size of the image, not enlarge it.

  • Scale Factor II: 116%

    To convert a percentage to a decimal scale factor, divide by 100. Thus, \(116\% = \frac{116}{100} = 1.16\). Since 1.16 is greater than 1, it will enlarge the image.

  • Scale Factor III: \(\frac{8}{5}\)

    The fraction \(\frac{8}{5}\) is equal to 1.6, which is greater than 1. Therefore, it will enlarge the image.

Step 3: Determine the Correct Answer

From the analysis, scale factors II and III will produce an image larger than the original.

Final Answer

\(\boxed{\text{II and III only}}\)

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