Question

two figures are dilations of each other
similar figures:
. corresponding sides are proportional.
. corresponding angles are equal.
are the corresponding sides of figures j and j proportional? complete each statement.
each side of figure j is 6 times as long as the corresponding side of figure j.
the scale factor is?

Explanation:

Step1: Understand the scale - factor concept

The scale factor of a dilation is the ratio of the length of a side of the dilated figure (\(J'\)) to the length of the corresponding side of the original figure (\(J\)).

Step2: Calculate the scale factor

We are given that each side of figure \(J'\) is \(k\) times as long as the corresponding side of figure \(J\). From the problem, if we assume the length of a side of \(J\) is \(2\) (for example, from the vertical side of \(J\)) and the length of the corresponding side of \(J'\) is \(6\). The scale factor \(k=\frac{\text{length of side in }J'}{\text{length of corresponding side in }J}\)

Let \(a\) be the length of a side in \(J\) and \(a'\) be the length of the corresponding side in \(J'\). Here, if \(a = 2\) and \(a'=6\), then \(k=\frac{a'}{a}\)

Substitute \(a = 2\) and \(a'=6\) into the formula: \(k=\frac{6}{2}=3\)

Answer:

The scale factor is \(3\)