The Four Transformations

• The Four Transformations refer to translation, rotation, reflection, and enlargement.
• A translation moves a shape to a new position without changing its size, shape or orientation. It is defined by a vector (a, b), where ‘a’ is the movement in the x direction and ‘b’ is the movement in the y direction.
• A rotation turns a shape around a fixed point (the center of rotation). The description of the rotation includes the angle (in degrees), the direction (clockwise or anticlockwise), and the center of rotation.
• A reflection flips a shape over a line, producing a mirror image. The line of reflection acts like a mirror and each point of the original figure is the same distance from the mirror as its reflection.
• An enlargement changes the size of a shape without altering its shape or orientation. It’s described by a center of enlargement and a scale factor. If the scale factor is greater than 1, the shape gets bigger. If it’s between 0 and 1, the shape gets smaller.
• It’s important to remember that all of these transformations can be combined. For instance, a shape could be translated, then reflected or enlarged, then rotated.
• To perform any of these transformations accurately, it is key to use a ruler and compass, particularly for finding the center of rotation and drawing reflected or enlarged shapes.
• These four transformations are a fundamental concept in geometry, underpinning many other topics and concepts. Mastery of these transformations will aid with other topics such as congruent shapes, symmetry, and coordinates.