1. 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.