Question

part b
the distance between point o and point r is 9 centimeters. what is the distance between point o and the image of point r under a dilation with center o and scale factor \\( \frac { 1 } { 3 } \\)?
\\( \square \\) centimeters

Explanation:

Step1: Recall the formula for dilation

The formula for the distance of the image of a point \(P\) from the center of dilation \(O\) is \(d'=k\times d\), where \(d\) is the original distance from \(O\) to \(P\), \(k\) is the scale factor, and \(d'\) is the distance from \(O\) to the image of \(P\).

Step2: Substitute the given values

We are given that \(d = 9\) centimeters and \(k=\frac{1}{3}\). Substituting these values into the formula \(d'=k\times d\), we get \(d'=\frac{1}{3}\times9\).

Step3: Calculate the result

\(\frac{1}{3}\times9=\frac{9}{3}=3\)

Answer:

3