One transformation after another, the points that never move, and what a negative scale factor does.
What you will learn
- Carry out two transformations in order
- Find the single transformation that does the same as two
- Find invariant points
- Enlarge by a negative scale factor (Higher)
One after another
For a combined transformation, do the first one, then apply the second one to the image.
The order matters: a reflection then a translation usually lands somewhere different from the translation then the reflection.
For example, (1, 2) reflected in the y-axis, then translated 3 right, goes to (−1, 2) and then (2, 2); translated first, then reflected, it goes to (4, 2) and then (−4, 2).
- P(3, 1): reflect in the x-axis, then rotate 90° anticlockwise about the origin
- Reflect: (3, 1) → (3, −1)
- Rotate: (x, y) → (−y, x), so (3, −1) → (1, 3)
- One map does both: (3, 1) → (1, 3) is a reflection in y = x
To name the single transformation, follow two or three points through both steps and ask which one transformation sends every point to the same place.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- One after another
- Invariant points
- Negative scale factors (Higher)
- Try it: First question
8 practice questions, marked as you go; about 25 minutes in all.
Key terms
Invariant
In this unit: Transformations, congruence and similarity
Translations, reflections, rotations and enlargements on a grid and how to describe them fully, combined transformations and invariant points, the congruence conditions, and similar shapes with their length, area and volume scale factors.
- Translations and reflections
- Rotations and enlargements
- Combined transformations and negative scale factors
- Congruent triangles
- Similar shapes and solids