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A second set of combined transformations questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
The point (1, 6) is translated by (2, -3) and then reflected in the x-axis. Where does it end up?
Answer: (3, -3)
Two translations, (3, 1) and then (-1, 4), are made one after the other. What single translation is equivalent?
Answer: (2, 5)
Two reflections are made in the parallel lines x = 2 and x = 7. How many units is the single translation?
Answer: 10
Two reflections are made in mirror lines that cross at the origin at 20 degrees to each other. Through what angle, in degrees, is the equivalent rotation?
Answer: 40
A shape is enlarged with scale factor 2 and then enlarged with scale factor 3, both about the same centre. What is the scale factor of the single enlargement?
Answer: 6
A shape is rotated 60 degrees anticlockwise about a point and then another 60 degrees anticlockwise about the same point. What is the angle of the single rotation, in degrees?
Answer: 120
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Shape A is reflected in the line x = 1. The image is then reflected in the line x = 4. Describe the single transformation that takes A to the final image.
Answer: translation (6, 0)
Short one-step questions. Pick an option before you open the answer.
In reflect then translate, which transformation is done first?
The reflection. The second transformation acts on the image of the first. The reflection. The second transformation acts on the image of the first.
Does the order of two transformations usually matter?
Yes. Swapping the order usually gives a different image. Yes. Swapping the order usually gives a different image.
What do two reflections in parallel lines make?
A translation, at right angles to the mirror lines, of twice the distance between them. A translation, at right angles to the mirror lines, of twice the distance between them.
What do two reflections in lines that cross make?
A rotation about the crossing point through twice the angle between the lines. A rotation about the crossing point through twice the angle between the lines.
What do two translations make?
One translation whose vector is the sum of the two vectors. One translation whose vector is the sum of the two vectors.
What do two enlargements about the same centre make?
One enlargement whose scale factor is the product of the two scale factors. One enlargement whose scale factor is the product of the two scale factors.
What is the rule for reflection in the x-axis?
(x, y) goes to (x, -y). (x, y) goes to (x, -y).
What is the rule for a rotation of 90 degrees anticlockwise about the origin?
(x, y) goes to (-y, x). (x, y) goes to (-y, x).
What is the rule for a half turn about the origin?
(x, y) goes to (-x, -y). (x, y) goes to (-x, -y).
What does a full description of a rotation include?
The centre, the angle and the direction. The centre, the angle and the direction.
What does a full description of a reflection include?
The equation of the mirror line. The equation of the mirror line.
What does a full description of an enlargement include?
The centre of enlargement and the scale factor. The centre of enlargement and the scale factor.
Why is a list of two transformations not a single transformation?
The question asks for one transformation, so the answer must name one. The question asks for one transformation, so the answer must name one.
How can you check a single transformation you have found?
Apply it to a point you tracked and see if it lands on the same finishing point. Apply it to a point you tracked and see if it lands on the same finishing point.
A half turn then a translation is what kind of single transformation?
A half turn about a new centre. A half turn about a new centre.
AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.