1. **Stating the problem:** We have a polygon with vertices at points $(1,9)$, $(4,9)$, $(4,7)$, $(2,4)$, and $(2,1)$. We want to increase its size by a factor of $\frac{3}{2}$. This means every coordinate of the polygon will be scaled by $\frac{3}{2}$ from the origin $(0,0)$. 2. **Formula used:** To scale a point $(x,y)$ by a factor $k$, the new point $(x',y')$ is given by: $$ (x',y') = (k \times x, k \times y) $$ Here, $k = \frac{3}{2}$. 3. **Applying the scale factor to each vertex:** - For $(1,9)$: $$ \left(\frac{3}{2} \times 1, \frac{3}{2} \times 9\right) = \left(\frac{3}{2}, \frac{27}{2}\right) = (1.5, 13.5) $$ - For $(4,9)$: $$ \left(\frac{3}{2} \times 4, \frac{3}{2} \times 9\right) = \left(6, \frac{27}{2}\right) = (6, 13.5) $$ - For $(4,7)$: $$ \left(\frac{3}{2} \times 4, \frac{3}{2} \times 7\right) = (6, 10.5) $$ - For $(2,4)$: $$ \left(\frac{3}{2} \times 2, \frac{3}{2} \times 4\right) = (3, 6) $$ - For $(2,1)$: $$ \left(\frac{3}{2} \times 2, \frac{3}{2} \times 1\right) = (3, 1.5) $$ 4. **Final answer:** The new polygon vertices after scaling by $\frac{3}{2}$ are: $$(1.5, 13.5), (6, 13.5), (6, 10.5), (3, 6), (3, 1.5)$$ This means the polygon is enlarged by 1.5 times in both the $x$ and $y$ directions, keeping the shape but increasing its size proportionally.