1. The problem is to understand the concept of enlargement in geometry. 2. Enlargement is a transformation that changes the size of a shape but keeps its shape and angles the same. 3. The formula for enlargement with center $O$ and scale factor $k$ is: if a point $P$ is enlarged to $P'$, then $$OP' = k \times OP$$ where $OP$ and $OP'$ are distances from the center $O$ to points $P$ and $P'$ respectively. 4. Important rules: - If $k > 1$, the shape gets larger. - If $0 < k < 1$, the shape gets smaller. - The center of enlargement stays fixed. - Angles remain unchanged. 5. For example, if a triangle has side length 4 and is enlarged by a scale factor of 3, the new side length is $$4 \times 3 = 12$$. 6. This means the enlarged shape is similar to the original but scaled by the factor $k$. 7. Enlargement helps in understanding similarity, scale models, and maps.