Drag the gold handle to move the mirror line, the centre or the vector, press ▶ Watch it to see the shape move, or try 🎯 Match the target: work out which transformation puts the image exactly on the green outline. The letter F makes flips and turns easy to spot.
- What are the four transformations in maths?
- Reflection flips a shape in a mirror line, rotation turns it about a centre, translation slides it by a vector, and enlargement scales it from a centre by a scale factor. The first three keep the size and shape; enlargement changes the size.
- How do you reflect a shape in a mirror line?
- Take each corner and measure its perpendicular distance to the mirror line. Mark the image the same distance on the other side, on the same perpendicular. Join the new points. In the x-axis, (x, y) becomes (x, −y); in the y-axis it becomes (−x, y).
- What do you need to describe a rotation?
- Three things: the angle (90°, 180°…), the direction (clockwise or anticlockwise) and the centre of rotation. Without the centre, several different rotations share the same angle. Every point stays the same distance from the centre as it turns.
- How does a column vector translate a shape?
- A vector (a, b) moves every point a units across and b units up, or down if b is negative. So (2, 3) under translation by (4, −1) goes to (6, 2). The shape is not turned, flipped or resized.
- What does a negative scale factor do?
- The image lands on the opposite side of the centre of enlargement, upside down. Scale factor −2 makes lengths twice as long and flips each point through the centre. Scale factor −1 gives the same image as a 180° rotation about that centre.
- What is the difference between congruent and similar shapes?
- Congruent shapes are identical in size and shape; reflections, rotations and translations produce congruent images. Similar shapes have the same shape but different sizes, as an enlargement gives. Lengths scale by the scale factor k and areas by k².