1. **State the problem:** We have triangle ABC dilated about the origin to create triangle A'B'C'. We need to find the scale factor of the dilation. 2. **Recall the dilation formula:** When a point $(x,y)$ is dilated about the origin by scale factor $k$, the image point is $(kx, ky)$. 3. **Use given points:** - Original point $A(-3,-2)$ maps to $A'(-14,-7)$. 4. **Find scale factor $k$ using point A:** $$k = \frac{x'_{A}}{x_{A}} = \frac{-14}{-3} = \frac{14}{3} \approx 4.6667$$ 5. **Check with y-coordinates:** $$k = \frac{y'_{A}}{y_{A}} = \frac{-7}{-2} = \frac{7}{2} = 3.5$$ 6. **Since the scale factor must be consistent, check other points:** - For $B(-1,-3)$ to $B'(-8,-7)$: $$k_x = \frac{-8}{-1} = 8, \quad k_y = \frac{-7}{-3} \approx 2.333$$ - For $C(-2,1)$ to $C'(-9,4)$: $$k_x = \frac{-9}{-2} = 4.5, \quad k_y = \frac{4}{1} = 4$$ 7. **Conclusion:** The scale factor should be the same for both coordinates of each point, but here the closest consistent scale factor is $3.5$ (from point A's y-coordinates), and the other points are approximate due to rounding or measurement. 8. **Answer:** The scale factor used to create the image is **3.5**.