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 and scale factor 1/3?
centimeters.

Explanation:

Step1: Recall the property of dilation

When a point is dilated with a center \(O\), the distance from the center \(O\) to the image of the point is equal to the scale factor multiplied by the original distance from \(O\) to the point. Let the original distance \(d = 9\) centimeters and the scale factor \(k=\frac{1}{3}\).

Step2: Calculate the new distance

The formula for the distance \(D\) after dilation is \(D=k\times d\). Substitute \(k = \frac{1}{3}\) and \(d = 9\) into the formula: \(D=\frac{1}{3}\times9\).
Since \(\frac{1}{3}\times9=\frac{9}{3}=3\).

Answer:

3