Enlargement in the Cartesian Plane

What is Enlargement?

Enlargement is a type of transformation that changes the size of a shape but keeps its proportions the same. It involves a scale factor and a center of enlargement.

• Scale Factor: Determines how much larger or smaller the image will be compared to the original shape. If the scale factor is greater than 1, the shape enlarges. If it's between 0 and 1, the shape reduces.
• Center of Enlargement: The fixed point in the plane from which the shape is enlarged or reduced.

How to Perform Enlargement

1. Identify the Center of Enlargement: This point can be inside, outside, or on the shape.
2. Determine the Scale Factor: Decide how much larger or smaller the shape should be.
3. Draw Lines: Connect each vertex of the original shape to the center of enlargement.
4. Measure and Mark: From the center, measure the distance to each vertex, multiply by the scale factor, and mark the new points.
5. Connect the New Points: Form the enlarged or reduced shape.

Examples

Example 1: Enlarge a Triangle

Given a triangle with vertices at $(1, 2), (3, 2), (2, 4)$, enlarge it by a scale factor of 2 with the center of enlargement at $(0, 0)$.

Example 2: Reduce a Rectangle

Given a rectangle with vertices at $(2, 3), (6, 3), (6, 5), (2, 5)$, reduce it by a scale factor of $\frac{1}{2}$ with the center of enlargement at $(0, 0)$.