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Answered

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Square A'B'C'D' is the image of square ABCD under a dilation from center O¹ by scale factor r. Square A''B''C''D'' is the image of square A'B'C'D' under a dilation from center O² by scale factor 1/4. The side lengths of square A''B''C''D'' are 1/8 of the corresponding side lengths of square ABCD. What is the scale factor r?​

Sagot :

The value of r is given from the combined scale factor transforms ABCD to

A''B'C''D'' and the scale factor that transforms ABCD to A'B'C'D'.

The Correct Response;

  • [tex]\displaystyle \underline{The \ scale \ factor \ r \ is \ \frac{1}{2} }[/tex]

Method by which the value of r is found;

Scale factor of dilation of square ABCD to give the image A'B'C'D' = r

Scale factor of dilation to give square A''B''C''D'' from A'B'C'D' = 1/4

Side lengths of square A''B''C''D'' = 1/8 × Side lengths of square ABCD

Required:

The value of the scale factor r.

Solution:

From the question, we have;

Scale factor of dilation of square ABCD to give the image A''B''C''D'' = 1/8

Combining the sale factors gives;

  • [tex]\displaystyle \mathbf{r \times \frac{1}{4} } = \frac{1}{8}[/tex]

[tex]\displaystyle r = 4 \times \frac{1}{8} = \frac{1}{2}[/tex]

  • [tex]\displaystyle The \ scale \ factor \ \underline{ r = \frac{1}{2} }[/tex]

Learn more about the scale factor of a dilation here:

https://brainly.com/question/10618542

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