Rigid transformations on a coordinate plane
Welcome to the session! Before we dive into the world of moving shapes around the coordinate grid, I'd love to know a bit about your background. This helps me tailor our pace and examples perfectly for you.
I know basics like plotting points, but transformations are new to me.
Plotting points is the perfect foundation for this because every transformation we do is just a rule for moving those very points! Let's preview our game plan for mastering these movements on the grid.
Your path
Translations on the Coordinate Plane
Reflections on the Coordinate Plane
Rotations on the Coordinate Plane
Sequences of Transformations
What Makes a Transformation Rigid
To kick things off, let's look at the word rigid. In everyday life, if something is rigid, it is stiff and cannot be bent or reshaped. It is exactly the same in geometry!
A (sometimes called an isometry) is a way of moving a geometric figure on a plane so that its overall shape and size remain completely unchanged.
A geometry visual showing three triangles on a coordinate grid to illustrate rigid versus non-rigid transformations.
As you can see, when we apply a rigid transformation, we can slide the shape, flip it, or spin it around. But we are strictly forbidden from stretching, shrinking, or bending it.
Before we look at the three main types, does this 'shape and size preservation' rule make intuitive sense?