A dilation with center (0,0) and scale factor "k" is applied to a polygon. What dilation can you apply to the image to return it to the original preimage?

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03-05-2015
Mathematics

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A dilation with center (0,0) and scale factor "k" is applied to a polygon. What dilation can you apply to the image to return it to the original preimage?

Sagot :

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RedRicinidn RedRicinidn · Answer 1 · 2015-05-03T19:25:51-04:00

So when we scale up this image, all points' distances from the center are multiplied by [tex]k[/tex]. We want to then put them back to where they were before.

Thinking about inverse operations, we could just divide by [tex]k[tex], right? But the problem with having a scale factor is we can only multiply.

Think about fractions. Dividing by a fraction is the same as multiplying by the reciprocal, right?

So if we think of [tex]k[/tex] as [tex]\frac{k}1[/tex], then the opposite reciprocal would be [tex]\boxed{\frac{1}k}[/tex]

Sagot :

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