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 first endpoint $(-1,2)$ and its image $(-3,6)$.

Step2: Calculate the scale - factor

We know that $x'=kx$ and $y' = ky$. For the $x$ - coordinates: $-3=k\times(-1)$. Solving for $k$ gives $k = 3$. We can also check with the $y$ - coordinates: $6 = k\times2$. Solving $6 = 2k$ also gives $k = 3$.

Answer:

3