1. **State the problem:** We need to determine if the point (2,9) can be the center of enlargement that maps the smaller cross centered at (4,7) to the larger cross centered at (9,4). 2. **Understand enlargement:** An enlargement with center $C=(x_c,y_c)$ and scale factor $k$ maps any point $P=(x,y)$ to $P'=(x',y')$ such that: $$x' = x_c + k(x - x_c)$$ $$y' = y_c + k(y - y_c)$$ 3. **Apply to centers:** Let the smaller center be $P=(4,7)$ and the larger center be $P'=(9,4)$, and the proposed center of enlargement be $C=(2,9)$. 4. **Set up equations:** $$9 = 2 + k(4 - 2)$$ $$4 = 9 + k(7 - 9)$$ 5. **Simplify each:** - For $x$ coordinate: $$9 = 2 + 2k \implies 2k = 7 \implies k = 3.5$$ - For $y$ coordinate: $$4 = 9 + k(-2) \implies 4 - 9 = -2k \implies -5 = -2k \implies k = 2.5$$ 6. **Compare scale factors:** The $x$ and $y$ calculations give different scale factors ($3.5$ vs $2.5$), which is impossible for a single enlargement. 7. **Conclusion:** Since the scale factors do not match, (2,9) cannot be the center of enlargement mapping the smaller cross to the larger cross. **Final answer:** No, (2,9) is not the center of enlargement because the scale factors derived from the $x$ and $y$ coordinates are not equal, which violates the properties of enlargement.