Question

pq is the image of pq after a dilation centered at the origin. pq has endpoints at (-1, 2) and (0, 3). pq has endpoints at (-3, 6) and (0, 9). what is the scale factor of the dilation?

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 $x' = kx$ and $y'=ky$. We can use one of the endpoints. Let's use the endpoint $(-1,2)$ which is dilated to $(-3,6)$.

Step2: Calculate scale - factor

We know that if $x=-1$ and $x'=-3$, then from $x' = kx$, we substitute the values: $-3=k\times(-1)$. Solving for $k$ gives $k = 3$. We can double - check with the $y$ - coordinates. If $y = 2$ and $y'=6$, then from $y'=ky$, we have $6=k\times2$, which also gives $k = 3$.

Answer:

$3$