Translation and reflection are two important types of changes we can make in math. They are very different from each other.

Translation:

• What It Is: A translation simply moves an object from one place to another without changing its shape or position.

• How It Works: Imagine you have a triangle. You want to move it to the right by 3 spaces and up by 2 spaces. Every point of the triangle moves the same way.

  If you have a point at $(x, y)$, and you move it by $(a, b)$, the new point will be $(x + a, y + b)$. So, moving the triangle keeps it just the same, but in a new spot.

Reflection:

• What It Is: A reflection flips an object over a line, like a mirror. This makes a mirror image of the object.

• How It Works: For example, if you reflect a triangle over the y-axis (the vertical line), the points on the triangle will flip to the other side of the y-axis. So, if a point was at $(x, y)$, after the reflection, it will be at $(-x, y)$.

To sum it up, translations move objects around while keeping their shape, and reflections create a mirror image by flipping them across a line. This difference is what makes learning about transformations in math so fun!