What is enlargement? An enlargement is a geometric transformation that changes the size of a shape while keeping its proportions and internal angles exactly the same. Despite the name "enlargement," this process can make a shape bigger or smaller! The resulting image is similar to the original object, but not congruent. Think of pinching to zoom into a photograph on a phone screen, or using a projector to display a laptop screen onto a wall.
To perform an enlargement, you must know two pieces of information:
- The center of enlargement: The fixed anchor point from which lines are drawn through all vertices of the shape to expand or shrink it.
- The scale factor (\(k\)): The multiplier value used to alter the side lengths.
How Scale Factors Work:
- If \(k > 1\), the shape grows larger (e.g., \(k = 2\) means the image is twice as large as the original).
- If \(0 < k < 1\), the shape shrinks smaller (e.g., \(k = \frac{1}{2}\) means the image is half the original size).
\[ \text{Scale Factor } (k) = \frac{\text{Image Side Length}}{\text{Corresponding Object Side Length}} \]