Final answer:
The equivalent single scale factor for dilating the original rectangle first by 9 and then by 1/8 is the product of the two scale factors, which is 9 × (1/8) = 1.125.
Step-by-step explanation:
To find the equivalent single scale factor for the two given dilations of a rectangle, you multiply the two individual scale factors together. The rectangle is first dilated using a scale factor of 9, and then it is subsequently dilated by a scale factor of 1/8. To combine these two scale factors into one, you would perform the following calculation:
Combined scale factor = First scale factor × Second scale factor
Combined scale factor = 9 × (1/8) = 9/8
Since 9 × (1/8) equals 9/8, and 9 divided by 8 equals 1.125, the combined scale factor is 1.125. However, if our intention is to find the scale factor that would directly take the original rectangle to the final rectangle after both dilations have been applied, then:
Final scale factor = (Original to first image scale factor) × (First image to final image scale factor)
Final scale factor = 9 × (1/8)
Final scale factor = 1.125
The calculation shows that a single dilation with a scale factor of 1.125 would have the same effect as applying two consecutive dilations with scale factors of 9 and 1/8 respectively.