1. **Stating the problem:** We have two shapes on squared paper. We need to enlarge each shape by the given scale factors: (a) scale factor $\frac{1}{2}$ and (b) scale factor $4$. We also discuss what happens to side lengths and angles when enlarging by a positive number less than 1. 2. **Formula for enlargement:** When enlarging a shape by a scale factor $k$, each side length is multiplied by $k$. The angles remain the same because enlargement is a similarity transformation. 3. **Enlarging shape (a) by scale factor $\frac{1}{2}$:** - Each side length is multiplied by $\frac{1}{2}$. - For example, if a side length is $s$, the new length is $s \times \frac{1}{2} = \frac{s}{2}$. - Angles remain unchanged. 4. **Enlarging shape (b) by scale factor $4$:** - Each side length is multiplied by $4$. - For example, if a side length is $s$, the new length is $s \times 4 = 4s$. - Angles remain unchanged. 5. **Discussion:** - When enlarging by a positive number less than 1 (like $\frac{1}{2}$), the shape becomes smaller because side lengths decrease. - Angles do not change because enlargement preserves shape similarity. - When enlarging by a number greater than 1 (like $4$), the shape becomes larger because side lengths increase. **Final answer:** Enlarging by scale factor $k$ multiplies all side lengths by $k$ and keeps all angles the same. If $0 < k < 1$, the shape shrinks; if $k > 1$, the shape enlarges.