1. **Problem Statement:** Identify the center and scale factor of a dilation and correct any errors in the student's identification. 2. **Given:** Center: $(0,1)$ Scale Factor: $k=2$ 3. **Understanding Dilation:** A dilation with center $(x_c,y_c)$ and scale factor $k$ transforms any point $(x,y)$ to a new point $(x',y')$ using the formulas: $$x' = x_c + k(x - x_c)$$ $$y' = y_c + k(y - y_c)$$ 4. **Check the Center:** The center is given as $(0,1)$, which means all points are scaled relative to this point. 5. **Check the Scale Factor:** The scale factor $k=2$ means each point moves twice as far from the center. 6. **Common Student Error:** Sometimes students confuse the center or scale factor or apply the scale factor incorrectly. 7. **Verification Example:** Take a point $R$ at $(x,y)$ and calculate $R'$: $$x' = 0 + 2(x - 0) = 2x$$ $$y' = 1 + 2(y - 1) = 1 + 2y - 2 = 2y - 1$$ 8. **Interpretation:** The transformed point $R'$ should be at $(2x, 2y - 1)$. 9. **Conclusion:** The student's identification of center $(0,1)$ and scale factor $k=2$ is correct if the transformed points satisfy the above formula. If the student's error was in applying the scale factor or center incorrectly, the correction is to use the formulas above. **Final answer:** Center: $(0,1)$ Scale Factor: $k=2$