Understanding Enlargements and Other Transformations in Geometry

In geometry, different changes can be made to shapes. Two main types are enlargements and other transformations. Let’s look at what makes them different.

1. What They Are:

   • Enlargement: This is when a shape gets bigger or smaller. It’s done evenly from a special point called the center of enlargement.
   • Other Transformations: These include moving (translations), turning (rotations), and flipping (reflections) a shape. They change where the shape is or how it looks, but not its size.

2. Scale Factor:

   • Enlargement: It uses something called a scale factor (let's call it $k$). If $k$ is more than 1, the shape grows bigger. If $k$ is between 0 and 1, the shape shrinks. For example, imagine a triangle with points at (2, 3), (4, 5), and (6, 7). If you enlarge it by a scale factor of 2, the new points will be (4, 6), (8, 10), and (12, 14).
   • Other Transformations: These don’t use scale factors. They just move or flip the shape without changing how big it is.

3. Center of Transformation:

   • Enlargement: There is always a special center from which distances to the shape change.
   • Other Transformations: There isn't a center. These changes happen based on directions (in translations) or lines (in reflections).

4. Properties:

   • Enlargement: The new shape looks similar to the original. The angles stay the same, but the sides change size based on the scale factor.
   • Other Transformations: These can keep distances the same (like translations and rotations) or keep the shape the same (like reflections).

Knowing these differences is important if you want to do well in geometry in Year 8.