Toolbox
A formula sheet plus reference tools for calculator, equation solver, units, elements, graphs and molecules.
Transformations
Translation, rotation, reflection and dilation: the original and its image share one grid, vertex by vertex.
Pick a shape and a transformation, then set the parameters. Rotation and dilation are about the origin.
Dashed outline is the original, solid is the image; arrows show the translation
| Vertex | Original | Image vertices |
|---|---|---|
| A | (1, 1) | (4, -1) |
| B | (4, 1) | (7, -1) |
| C | (1, 3) | (4, 1) |
- Rule
- (x, y) to (x + 3,; y + -2)
- Invariants
- shape, size and orientation unchanged
- 1Formula
Write the coordinate rule.
- 2Substitute
Apply it to one vertex as an example.
- 3Conclusion
Repeat the same rule for the other vertices.
Concept
Translation, rotation and reflection are rigid motions: shape and size stay the same, only position or orientation changes. Dilation is a similarity, so size changes.
Read the transformation from corresponding points: parallel equal segments mean translation, equal distances to a centre mean rotation, perpendicular bisectors mean reflection.
Going further
- Reflection in y = x
- The reflection of (x, y) in y = x is (y, x); reflection in the origin negates both coordinates.
Common mistakes
- A 180° rotation is the same as point symmetry about the origin.
- A negative scale factor sends the image to the opposite side of the origin.