Question

question 13
a dilation maps the point (8,12) to (4,6). what is the scale factor of the dilation?
(1)/(2)
4
2
3

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin, if a point $(x,y)$ is dilated to $(x',y')$, the scale - factor $k$ is given by $k=\frac{x'}{x}=\frac{y'}{y}$.

Step2: Calculate scale - factor using x - coordinates

We have the original point $(8,12)$ and the dilated point $(4,6)$. Using the x - coordinates, $x = 8$ and $x'=4$. Then $k=\frac{x'}{x}=\frac{4}{8}=\frac{1}{2}$.

Step3: Verify using y - coordinates

Using the y - coordinates, $y = 12$ and $y' = 6$. Then $k=\frac{y'}{y}=\frac{6}{12}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$