Combined transformations
Objective. Compare and perform sequences of transformations.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Combined transformations apply two or more moves, such as a reflection then a rotation, one after another to the same shape, and the order matters. Each transformation acts on the image produced by the previous step, not on the original shape again. A single combined transformation can sometimes be described as one equivalent transformation, such as two reflections in parallel lines being equivalent to a translation. Example: reflecting a point in the x-axis then translating it by (2, 0) moves (3, 4) first to (3, −4), then to (5, −4).
Worked example
A combined transformation reflects the point (2, 3) in the y-axis, then rotates the result 90° anticlockwise about the origin. Find the final image.
- 1Reflect (2, 3) in the y-axis: (x, y) becomes (−x, y), giving (−2, 3).
- 2Apply the rotation rule for 90° anticlockwise: (x, y) becomes (−y, x).
- 3Substitute the reflected point: (−3, −2).
- 4The final image after both transformations is (−3, −2).
Answer: (−3, −2)
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes apply both transformations to the original shape separately instead of applying the second transformation to the image of the first; always transform the result of the first step, not the starting shape.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.