Reflection, rotation and translation of a point
Move a point P on a grid by reflecting it in an axis, rotating it about the origin or sliding it. Read the coordinates of its image P′ and find the rule for each transformation.
Core concept
Each transformation changes coordinates by a rule: reflection in the x-axis (x, y) → (x, −y), in the y-axis (x, y) → (−x, y), rotation of 90° anticlockwise about O (x, y) → (−y, x), of 180° (x, y) → (−x, −y), and translation by (a, b) (x, y) → (x + a, y + b)
Topic: Coordinates and transformation
A transformation moves a shape, or a point, to a new place called its image. We write the image of P as P′. A reflection flips P over a mirror line: reflecting in the x-axis keeps x and changes the sign of y, so (3, 2) → (3, −2). A rotation turns P about a centre, here the origin O: a quarter turn anticlockwise (90°) takes (x, y) to (−y, x), and a half turn (180°) takes it to (−x, −y). A translation slides P without turning it: translating by (3, −2) adds 3 to x and takes 2 from y. With these rules you can find an image without drawing it.
What you will learn
- Reflect a point in the x-axis and in the y-axis.
- Rotate a point 90° and 180° about the origin.
- Translate a point by a given amount.
- Write the coordinate rule for each transformation.
Before you start
- Plot points with positive and negative coordinates.
Materials
- Graph paper, a ruler and tracing paper
Equipment
- None
Procedure
- Reflect P(3, 2) in the x-axis and record.
- Reflect it in the y-axis and record.
- Rotate it 90° anticlockwise about O and record.
- Translate it by (3, −2), and record two different points.
How this simulation is simplified
- Rotations are about the origin O(0, 0).