Question

answer the question below. type your response in the space provided.
δrst is dilated about the origin, o, to create δrst. point r is located at (3, 9), and point r is located at (1.2, 3.6). which scale factor was used to perform the dilation?

Explanation:

Step1: Calculate the scale factor for the x - coordinate

The formula for scale factor \(k\) is \(k=\frac{x_{new}}{x_{original}}\).
For the x - coordinates, \(x_{original} = 3\) and \(x_{new}=1.2\). So \(k_x=\frac{1.2}{3}\)

$$k_x = 0.4$$

Step2: Calculate the scale factor for the y - coordinate

Using the formula \(k=\frac{y_{new}}{y_{original}}\).
For the y - coordinates, \(y_{original}=9\) and \(y_{new} = 3.6\). So \(k_y=\frac{3.6}{9}\)

$$k_y=0.4$$

Since the scale factor for a dilation about the origin is the same for both x and y coordinates (because dilation is a uniform transformation), we can confirm the scale factor.

Answer:

\(0.4\)