What are coordinate transformations?

Coordinate transformations are like switching maps when you're playing hide and seek, you’re still looking for the same person, but you use a different way to describe where they are.

Imagine you and your friend are playing in a big park. You both have maps of the park, one map shows how it looks from the north side, and the other shows it from the east side. When you look at the map from the north, your friend is at position (3, 4). But when you switch to the map from the east, their position changes to (5, 2). That’s a coordinate transformation, you’re still talking about the same spot in the park, just using different numbers because of a different view.

Sometimes you want to make problems easier. Like if you're trying to find your friend and one map is easier for counting steps than the other. A coordinate transformation lets you re-express where things are so that solving the problem becomes simpler, just like switching from a messy puzzle piece arrangement to a neater one.

Think of a robot moving around a room. It might use one set of coordinates when following instructions, but when it turns its head or moves, it uses another. That’s the same idea, coordinate transformations help robots (and people) understand movement and position from different angles.