Question

a triangle with vertices a(1,2), b(2,4), and c(3,6) is dilated to create a(2,4), b(4,8), and c(6,12). what is the dilation factor? a. 1/2 b. 3 c. 2 d. 2/3

Explanation:

Step1: Recall dilation - factor formula

The dilation factor $k$ for a point $(x,y)$ dilated to $(x',y')$ is given by $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming the center of dilation is the origin). We can use any of the corresponding - coordinates of the pre - image and image points. Let's use the $x$ - coordinates of point $A$ and $A'$.
For point $A(1,2)$ and $A'(2,4)$, we calculate the dilation factor using the $x$ - coordinates.

Step2: Calculate the dilation factor

$k = \frac{x_{A'}}{x_{A}}$, where $x_{A}=1$ and $x_{A'}=2$. So $k=\frac{2}{1}=2$. We can double - check using the $y$ - coordinates. For the $y$ - coordinates, $y_{A}=2$ and $y_{A'}=4$, and $k=\frac{y_{A'}}{y_{A}}=\frac{4}{2}=2$.

Answer:

c. 2