1. **State the problem:** We need to find the images of the vertices of triangle $\triangle PQR$ under a dilation centered at $(0,0)$ with scale factor 2. 2. **Recall the dilation formula:** For a dilation centered at the origin, the image of a point $(x,y)$ is given by: $$ (x', y') = (k \cdot x, k \cdot y) $$ where $k$ is the scale factor. 3. **Apply the dilation to each vertex:** - For $P(2,2)$: $$ P' = (2 \times 2, 2 \times 2) = (4,4) $$ - For $Q(2,6)$: $$ Q' = (2 \times 2, 2 \times 6) = (4,12) $$ - For $R(5,2)$: $$ R' = (2 \times 5, 2 \times 2) = (10,4) $$ 4. **Interpretation:** The image triangle $\triangle P'Q'R'$ has vertices $P'(4,4)$, $Q'(4,12)$, and $R'(10,4)$. 5. **Answer the multiple choice:** The graph that shows $\triangle PQR$ and its image $\triangle P'Q'R'$ with these vertices is option A (and B, which is the same as A).