Reflection and enlargement are two important changes we can make in geometry. Let’s break down how they work together.

1. Reflection: This change makes a shape look like a mirror image across a certain line, like the x-axis or y-axis. For example, if you have a point at $(x, y)$ and you reflect it across the y-axis, it becomes $(-x, y)$.

2. Enlargement: This change makes a shape bigger or smaller from a center point. We use something called a scale factor, which is a number that tells us how much to enlarge or reduce the size. For instance, if we enlarge a point by a factor of $2$ from the origin, a point like $(x, y)$ would become $(2x, 2y)$.

3. Combined Transformations: When we use both reflection and enlargement together, the order in which we do them is very important. If we reflect first and then enlarge, we get a different result than if we enlarge first and then reflect. This can change where the shapes end up and how big they are.

Example: Let’s say we reflect the point $(1, 2)$ over the y-axis. This gives us $(-1, 2)$. Now, if we enlarge this result by a factor of $2$, we get $(-2, 4)$.

But if we reverse the order—enlarging first—our point $(1, 2)$ becomes $(2, 4)$ when we enlarge it. Then, reflecting this point over the y-axis gives us $(-2, 4)$.

This shows us just how important the order of transformations is.