Question

reset the explore tool. press on any shape and create a reduction by entering a scale factor of $\frac{2}{3}$ for dilation. then press enter. enter the scale factor you should use to enlarge the shape to its original size: if a figure is dilated by a scale factor of $\frac{a}{b}$, where $a\
eq0$ and $b\
eq0$, a dilation by a scale factor of will transform the figure back to its original size.

Explanation:

Step1: Understand the concept of inverse scale factor

When a figure is dilated by a scale factor \(k_1=\frac{2}{3}\), to get back to the original size, we need to use the inverse of this scale factor. The formula for the inverse of a fraction \(\frac{a}{b}\) (where \(a
eq0,b
eq0\)) is \(\frac{b}{a}\).

Step2: Calculate the required scale factor

Given \(k_1 = \frac{2}{3}\), the scale factor \(k_2\) to enlarge it back to the original size is \(k_2=\frac{3}{2}\) since \(\frac{2}{3}\times\frac{3}{2}=1\). In general, if a figure is dilated by a scale factor of \(\frac{a}{b}\), a dilation by a scale factor of \(\frac{b}{a}\) will transform the figure back to its original size.

Answer:

\(\frac{3}{2}\)