Investigate what happens if: Rotation GM4.2 Extension Plenary Safiq has drawn a triangle with coordinates A(1, 2), B(3, 2) and C(1, 1). a What is the effect on the triangle if he reverses the coordinates, so that (1, 2) → (2, 1), (3, 2)→ (2, 3) and (1, 1) → (1, 1)? Investigate what happens if: b He reverses the signs of the coordinates (x, y) → (−x, −y). c He reverses the order and the signs of the coordinates (x, y) → (−y, −x). Preamble This investigation gives pupils the chance to revise their skills in identifying and describing reflections and rotations. It could be carried out in a large group, with various members investigating just one question, then pooling results and checking each other’s conclusions. Pupils may need reminding about what is required to describe a mapping fully. Possible content Rotation and reflection mappings. Resources Squared paper for drawing the triangles and its mappings. Solution/Notes a Reversing coordinates produces a reflection in the line y = x. b Reversing the signs of the coordinates produces a 180 rotation about the origin. c Reversing the order and sign of the coordinates produces a reflection in the line y = −x. The effect of other changes such as changing the sign on just one coordinate or swapping order and changing the sign of just one coordinate could be investigated for homework.