Understanding Transformations

Transformations are simply ways to change a shape's position or size - think of them as moving shapes around on a coordinate grid. There are four main types you need to master: translation, reflection, rotation, and enlargement.

Translation is the easiest one to grasp - it's just sliding a shape from one place to another without changing its size or orientation. When describing horizontal movement, remember that moving right is positive and left is negative. For vertical movement, up is positive and down is negative. Always describe translations using a vector that shows exactly how far the shape moves.

Reflection creates a mirror image of your shape across a line of reflection. The original and reflected shapes are always congruent (identical in size and shape). When answering exam questions, make sure you mention both "reflection" and the equation of the line you're reflecting across.

Rotation spins a shape around a fixed point called the centre of rotation. You'll typically work with angles of 90°, 180°, or 270°, and the direction can be clockwise or anticlockwise. Don't forget to identify all three key elements: the angle, direction, and centre point.

Pro tip: Always check your rotations by tracing the shape with your finger - it helps you visualise the movement!

Enlargement changes the size of a shape using a scale factor. Calculate this by dividing the new length by the old length. If the scale factor is greater than 1, the shape gets bigger; if it's between 0 and 1, it shrinks. Remember that invariant points are special spots that don't move during certain transformations - they're often key to solving tricky problems.