Enlargements - GCSE Maths

Fundamentals of Enlargement
📌 An enlargement changes the size of a shape but keeps all lengths in proportion.
📏 To be an enlargement, all lengths must be multiplied by the same scale factor (e.g., multiplying one side by 3 and another by 2 is *not* an enlargement).
📉 An enlargement can make a shape smaller; a scale factor less than 1 (like $1/2$ or $1/3$) results in a reduction.

Calculating and Applying Scale Factor (SF)
🚀 To enlarge a shape by a scale factor $k$, multiply all original lengths by $k$. For example, a shape with base 2 and height 3 enlarged by SF 2 results in a base of $2 \times 2 = 4$ and height $3 \times 2 = 6$.
✂️ To reduce a shape by a scale factor $k$ (where $k < 1$), multiply all original lengths by $k$. For example, halving lengths means using a scale factor of $1/2$.

Enlargement from a Center Point
📍 When enlarging from a specific center of enlargement (point P or Q), map corresponding points by repeating the journey from the center to the original point $k$ times (where $k$ is the scale factor).
↔️ For a scale factor of 3, the journey from the center to the original point is repeated three times in total.
🤏 For scale factors less than 1 (e.g., $1/2$), you calculate half the journey distance from the center to the original point to find the new point's location.
✅ A check method involves drawing a straight line from the center of enlargement through a point on the original shape; this line must pass through the corresponding point on the enlarged shape.

Describing an Enlargement Transformation
📝 Fully describing a single transformation that maps shape B to shape C (where size changes) requires three pieces of information: Enlargement, the scale factor, and the center of enlargement (given as coordinates).
📏 To find the scale factor when going from B to C, compare corresponding lengths (e.g., if height reduces from 4 units to 1 unit, the SF is $1/4$).
🌐 To find the center of enlargement, draw lines connecting corresponding vertices of the original and image shapes and find their point of intersection.

Key Points & Insights
➡️ The defining characteristic of an enlargement is the constant proportion applied to all linear dimensions.
➡️ Scale factors greater than 1 mean the shape gets bigger; factors between 0 and 1 mean the shape gets smaller.
➡️ When using a coordinate system, the center of enlargement (e.g., $(0, 0)$ or $(8, 3)$) dictates the final position of the enlarged shape.
➡️ When working with negative coordinates for the center of enlargement, fractional scale factors involve taking a fraction of the journey distance (e.g., half the distance) from the center to the original point.

📸 Video summarized with SummaryTube.com on Feb 25, 2026, 08:54 UTC