Step-by-step worked examples and graded practice questions on transformations — reflection, rotation, translation and enlargement, including negative and fractional scale factors.
📚 Foundation & Higher✅ 15 Practice Questions🔍 Full Worked Examples⚠️ Common Mistakes
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A reflection creates a mirror image of a shape in a line (the line of reflection). Every point moves to the opposite side of the line, staying the same perpendicular distance from it.
Worked Example 1 — Reflection
Reflect triangle A with vertices (1,1), (3,1), (1,4) in the x-axis. State the coordinates of the image.
1
Reflecting in the x-axis keeps the x-coordinate the same and negates the y-coordinate: (x, y) → (x, −y)
2
(1,1) → (1,−1), (3,1) → (3,−1), (1,4) → (1,−4)
AnswerA' = (1,−1), (3,−1), (1,−4)
Triangle A (teal) is reflected in the x-axis to give A' (dark). Notice each point stays the same distance from the x-axis, on the opposite side.
Translation
A translation slides a shape a fixed distance in a fixed direction, described by a vector. Every point moves by the same amount — the shape doesn't change size, rotate, or flip.
Worked Example 2 — Translation
Translate triangle A with vertices (1,1), (3,1), (1,3) by the vector (4, 2). State the coordinates of the image.
1
Add 4 to every x-coordinate and 2 to every y-coordinate.
2
(1,1) → (5,3), (3,1) → (7,3), (1,3) → (5,5)
AnswerA' = (5,3), (7,3), (5,5)
The dashed arrow shows the translation vector — every point moves by the same amount.
Rotation
A rotation turns a shape a given angle around a fixed point (the centre of rotation). You need to know the angle, the direction (clockwise or anticlockwise), and the centre.
Worked Example 3 — Rotation
Rotate triangle A with vertices (1,1), (3,1), (1,3) by 90° clockwise about the origin. State the coordinates of the image.
1
For a 90° clockwise rotation about the origin, the rule is: (x, y) → (y, −x)
2
(1,1) → (1,−1), (3,1) → (1,−3), (1,3) → (3,−1)
AnswerA' = (1,−1), (1,−3), (3,−1)
The dashed lines from the origin to A and A' show the 90° angle turned through — this is exactly what "rotate 90°" means: every point sweeps through a 90° angle about the centre of rotation.
Enlargement
An enlargement resizes a shape by a scale factor from a centre of enlargement. A scale factor greater than 1 makes the shape bigger; between 0 and 1 makes it smaller; a negative scale factor flips the shape to the opposite side of the centre as well as resizing it.
Worked Example 4 — Enlargement
Enlarge triangle A with vertices (1,1), (2,1), (1,2) by scale factor 2, centre (0,0). State the coordinates of the image.
1
With the centre at the origin, multiply each coordinate by the scale factor: (x, y) → (2x, 2y)
2
(1,1) → (2,2), (2,1) → (4,2), (1,2) → (2,4)
AnswerA' = (2,2), (4,2), (2,4)
The grey dashed lines run from the centre (0,0) to each point of A; the teal dashed lines continue the same distance again to reach A' — this is exactly what scale factor 2 means.
Practice questions
Work through each question before checking the answers. Where a question shows a shape and its image, the diagram is required to answer it.
Foundation (Grade 3–5)
Q1Reflect triangle A with vertices (2,1), (5,1), (2,3) in the x-axis. State the coordinates of the image.Foundation
Diagram for Question 1 (not to scale).
Q2Reflect triangle A with vertices (1,1), (4,1), (1,3) in the y-axis. State the coordinates of the image.Foundation
Q3Translate triangle A with vertices (1,1), (2,1), (1,3) by the vector (3,−2). State the coordinates of the image.Foundation
Diagram for Question 3 (not to scale). The dashed arrow shows the translation vector.
Q4The diagram shows triangle A and its image, triangle B. Describe fully the single transformation that maps A onto B.Foundation
Diagram for Question 4 (not to scale).
Q5Rotate triangle A with vertices (1,1), (2,1), (1,3) by 90° clockwise about the origin. State the coordinates of the image.Foundation
Diagram for Question 5 (not to scale).
Higher (Grade 5–7)
Q6Rotate triangle A with vertices (2,2), (5,2), (2,4) by 180° about the point (1,1). State the coordinates of the image.Higher
Diagram for Question 6 (not to scale). The centre of rotation, (1,1), is not the origin.
Q7Enlarge triangle A with vertices (1,1), (3,1), (1,2) by scale factor 3, centre (0,0). State the coordinates of the image.Higher
Diagram for Question 7 (not to scale).
Q8The diagram shows triangle A and its image, triangle B. Describe fully the single transformation that maps A onto B.Higher
Diagram for Question 8 (not to scale).
Q9Enlarge triangle A with vertices (2,1), (4,1), (2,2) by scale factor 3, centre (1,1). State the coordinates of the image.Higher
Q10Reflect triangle A with vertices (1,2), (4,1), (1,4) in the line y = x. State the coordinates of the image.Higher
Diagram for Question 10 (not to scale). The dashed line is y = x, the line of reflection.
Higher — Hard (Grade 8–9)
Q11Enlarge triangle A with vertices (1,1), (2,1), (1,2) by scale factor −2, centre (0,0). State the coordinates of the image.Grade 8–9
Diagram for Question 11 (not to scale). Notice the negative scale factor places the image on the opposite side of the centre.
Q12Enlarge triangle A with vertices (2,2), (6,2), (2,6) by scale factor ½, centre (2,2). State the coordinates of the image.Grade 8–9
Q13The diagram shows triangle A and its image, triangle B. Describe fully the single transformation that maps A onto B.Grade 8–9
Diagram for Question 13 (not to scale).
Q14Triangle A has vertices (1,1), (3,1), (1,2). It is reflected in the x-axis, then translated by the vector (2,3). Find the coordinates of the final image.Grade 8–9
Q15Triangle A with vertices (3,3), (5,3), (3,5) is rotated 90° anticlockwise about the point (2,2) to form triangle A'. State the coordinates of A', and describe the single transformation that would map A' back onto A.Grade 8–9
Answers
Foundation (Q1–Q5)
Q1A' = (2,−1), (5,−1), (2,−3)
Q2A' = (−1,1), (−4,1), (−1,3)
Q3A' = (4,−1), (5,−1), (4,1)
Q4Reflection in the x-axis
Q5A' = (1,−1), (1,−2), (3,−1)
Higher (Q6–Q10)
Q6A' = (0,0), (−3,0), (0,−2)
Q7A' = (3,3), (9,3), (3,6)
Q8Rotation 90° anticlockwise about the origin
Q9A' = (4,1), (10,1), (4,4)
Q10A' = (2,1), (1,4), (4,1)
Higher — Hard (Q11–Q15)
Q11A' = (−2,−2), (−4,−2), (−2,−4)
Q12A' = (2,2), (4,2), (2,4)
Q13Enlargement, scale factor −2, centre (0,0)
Q14(3,2), (5,2), (3,1)(reflect first: (1,−1),(3,−1),(1,−2), then translate)
Q15A' = (1,3), (1,5), (−1,3); the inverse is a 90° clockwise rotation about (2,2)
Common mistakes
Common Mistake 1
Giving an incomplete description of a transformation
A rotation needs the angle, direction and centre stated. An enlargement needs the scale factor and centre. A reflection needs the line of reflection. Missing any of these loses marks even if you've identified the right type of transformation.
Common Mistake 2
Confusing rotation direction
Clockwise and anticlockwise rotations by the same angle give different images (unless the angle is 180°). Always check which direction the shape has actually turned before naming it.
Common Mistake 3
Forgetting a negative scale factor flips the shape
A negative scale factor doesn't just resize — it also moves the image to the opposite side of the centre of enlargement. Forgetting this flip is a common Grade 8–9 error.
Common Mistake 4
Using the wrong centre when enlarging
Every point's new position depends on its distance from the centre of enlargement, not the origin, unless the centre happens to be the origin. Always measure from the given centre.
Exam tips
💡 Exam Tip 1
Plot points on the grid rather than working purely algebraically
Even if you know the coordinate rule, plotting the shape helps you catch mistakes — especially for rotations and negative enlargements, which are easy to get backwards.
💡 Exam Tip 2
State the transformation type first, then the details
Structure your answer as "Rotation, 90° clockwise, centre (0,0)" — naming the type first makes it clear you've identified it correctly before adding specifics.
💡 Exam Tip 3
Check your image is the right size and orientation
After transforming a shape, a quick sanity check (is it bigger or smaller? does it look rotated or flipped?) catches many arithmetic slips before you finalise an answer.
💡 Exam Tip 4
For combined transformations, do them one at a time
Apply the first transformation fully, find the intermediate image, then apply the second transformation to that image — don't try to combine both steps at once.
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