Question

triangle abc has vertices a(2, 4), b(0, -4), and c(-2, -2). it is dilated with a center at (0, 0) to produce triangle abc with vertices a(12, 24), b(0, -24), and c(-12, -12). what is the scale factor of the dilation?

Explanation:

Step1: Recall scale - factor formula

For a dilation with center at the origin $(0,0)$, if a point $(x,y)$ is dilated to $(x',y')$, the scale factor $k$ can be found using the formula $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$ and $y
eq0$). We can use any vertex. Let's use vertex $A$.

Step2: Calculate scale - factor using vertex $A$

For vertex $A(2,4)$ and its image $A'(12,24)$. Using the $x$ - coordinates, $k = \frac{x_{A'}}{x_{A}}=\frac{12}{2}=6$. Using the $y$ - coordinates, $k=\frac{y_{A'}}{y_{A}}=\frac{24}{4}=6$.

Answer:

$6$