Question

the vertices for quadrilateral abcd are (0, 9), (9, 0), (0, -9), and (-9, 0). 10. what is the scale factor of the dilation?

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation from a point $(x,y)$ to its image $(x',y')$ centered at the origin is given by $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$ and $y
eq0$). Let's take point $A(0,9)$ and its image $A'(0, 3)$.

Step2: Calculate the scale factor

We know that for a dilation centered at the origin, if we consider the $y$ - coordinates of point $A(0,9)$ and $A'(0,3)$. Using the formula $k = \frac{y_{A'}}{y_{A}}$, substituting $y_{A}=9$ and $y_{A'}=3$, we get $k=\frac{3}{9}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$