Combining translations and rotations is a fun part of Year 8 math!

When you think about transformations, imagine how shapes can move on a grid. It’s like playing a game with pieces on a board!

Here’s how to combine them:

1. Understand Each Transformation:

   • Translation: This means sliding the shape in a certain direction. Imagine moving all parts of the shape the same distance and direction, like pushing a puzzle piece.
   • Rotation: This means turning the shape around a fixed point, usually the center or a point on the shape itself. You pick an angle that tells you how far to turn it, like spinning a coin.

2. Order Matters:

   • The order in which you combine these movements is important! If you translate first and then rotate, the final shape will be different than if you rotate first and then translate.

3. Practical Example:

   • Let’s say you have a triangle at points A(1, 2), B(3, 2), and C(2, 4).
     • If you translate it 3 units to the right and 2 units up, the points would change to A'(4, 4), B'(6, 4), and C'(5, 6).
     • Now, if you rotate this new triangle 90 degrees to the right around the origin, you would follow the rules for rotation.

In summary, by playing with the order of translation and rotation, you can create some really cool shapes! Just keep track of your points, and you’ll start to see how these movements work together.