Question

reset the explore tool. press on any shape and create an enlargement by entering a scale factor of 2 for dilation. then press enter.
enter the scale factor you should use to reduce the shape to its original size:

reset the explore tool. press on any shape and create a reduction by entering a scale factor of \\( \frac { 1 } { 5 } \\) for dilation. then press enter.

enter the scale factor you should use to enlarge the shape to its original size:

Explanation:

Step1: Recall the relationship between scale factors for enlargement and reduction

If a shape is enlarged by a scale factor \(k\), to get back to the original size, the reduction scale factor is \(\frac{1}{k}\). If a shape is reduced by a scale factor \(m\), to get back to the original size, the enlargement scale factor is \(\frac{1}{m}\).

Step2: Calculate the scale factor for the first case

Given the enlargement scale factor \(k = 2\). Using the formula for the reduction scale factor \(s_1=\frac{1}{k}\), we substitute \(k = 2\) into the formula. So \(s_1=\frac{1}{2}\).

Step3: Calculate the scale factor for the second case

Given the reduction scale factor \(m=\frac{1}{5}\). Using the formula for the enlargement scale factor \(s_2=\frac{1}{m}\), we substitute \(m = \frac{1}{5}\) into the formula. So \(s_2 = 5\).

Answer:

For the first blank: \(\frac{1}{2}\)
For the second blank: \(5\)