Question

the pre - image (abcd) is dilated to become the image (abcd). the origin is the center of dilation. what scale factor is used to create the dilation?

Explanation:

Step1: Select a pair of corresponding points

Let's take point $A(1,4)$ and its image $A'(2,8)$.

Step2: Calculate the scale - factor for the x - coordinates

The formula for the scale factor $k$ in a dilation centered at the origin for the x - coordinate is $k=\frac{x_{image}}{x_{pre - image}}$. For points $A$ and $A'$, $x_{pre - image}=1$ and $x_{image}=2$, so $k_x=\frac{2}{1} = 2$.

Step3: Calculate the scale - factor for the y - coordinates

The formula for the scale factor $k$ in a dilation centered at the origin for the y - coordinate is $k=\frac{y_{image}}{y_{pre - image}}$. For points $A$ and $A'$, $y_{pre - image}=4$ and $y_{image}=8$, so $k_y=\frac{8}{4}=2$.
Since the scale factor is the same for both x and y coordinates, the scale factor of the dilation is 2.

Answer:

2