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: Understand the relationship between scale factors

When a shape is enlarged by a scale factor \(k_1\) and then needs to be reduced back, the required scale factor \(k_2\) is the reciprocal of \(k_1\). Similarly, when a shape is reduced by a scale factor \(k_3\) and then needs to be enlarged back, the required scale factor \(k_4\) is the reciprocal of \(k_3\).

Step2: Calculate the scale factor for the first case

Given the enlargement scale factor \(k_1 = 2\). The scale factor to reduce it back to original size is \(k_2=\frac{1}{2}\) since \(2\times\frac{1}{2} = 1\) (which means the shape returns to its original size).

Step3: Calculate the scale factor for the second case

Given the reduction scale factor \(k_3=\frac{1}{5}\). The scale factor to enlarge it back to original size is \(k_4 = 5\) since \(\frac{1}{5}\times5=1\) (which means the shape returns to its original size).

Answer:

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