Question

Which scale factors produce a contraction under a dilation of the original image? Select each correct answer. ​−6​ ​−0.5​ 0.5 6

Answer 1

A contraction would make the image smaller.

A negative number reflects the image and changes the size based on the number.

To make an image smaller the factor needs to be less than 1

so -0.5 and 0.5 would make the image smaller since 0.5 is less than 1.

Answer 2

The scale factors 0.5 and -0.5 are the values to determine the contraction under the dilation of original image.

The scale factor is the ratio of the corresponding sides of two similar objects. Generally, it is used to relate the size of one object or geometry with respect to the other.

• Consider an original geometry, say a triangle ABC. Also consider another triangle A'B'C'. Then, scale factor will be given as the ratio of  adjacent sides of triangles. That is,

       

          $\rm Scale \;\rm Factor = \dfrac{AC}{A'C'}$

• As per the given problem, for scale factor equal to 1, says that the original figure(figure ABC) and the reference figure (figure of A'B'C') has the same size. Anything less that 1, shows the contraction of reference image with respect to original image.
• here, 0.5 and -0.5 are the values less than 1. So they will determine the required contraction.

Thus, we can conclude that the scale factors 0.5 and -0.5 are the values to determine the contraction under the dilation of original image.

Learn more about scale factors here:

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