Transformations & Vectors

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Corbett MathsTransformations — rotation, reflection, translation

Corbett MathsVectors — addition, subtraction and proof

GCSE Maths TutorRotations | Drawing and Describing Rotations | Transformations | GCSE Maths Tutor

GCSE Maths TutorVectors & Vector Proofs (Vector Geometry) | Grade 9 Maths Series | GCSE Maths Tutor

Key facts & methods

Transformations

Translation: described by a column vector. E.g. (3/−2) means 3 right, 2 down.
Rotation: described by centre, angle and direction (CW or anticlockwise). Default is anticlockwise.
Reflection: described by the mirror line (e.g. y=x, x=2, y=−1).
Enlargement: described by centre and scale factor (SF). SF>1: enlargement. 0
Congruent shapes: same size and shape (rotation, reflection, translation preserve size). Similar: same shape only (enlargement).

Vectors

Vectors have magnitude AND direction. Written in bold or with underline: a, a̲.
Column vector notation: (x/y) means x right, y up (negative values go left/down).
Add: add corresponding components. Scalar multiply: multiply each component.
Magnitude of vector (x/y) = √(x²+y²).
Vector geometry: if OA = a and OB = b, then AB = b − a.
Midpoint M of AB: OM = a + ½(b−a) = ½(a+b).

Exam questions — 5 questions · 12 marks · Edexcel 4MA1 style

3 marksDescribe transformation4MA1 Set 1 P1H Q5b style ✏️ No calculator

On a coordinate grid, shape A maps to shape B. Shape A has vertices at (1,1), (3,1), (3,2). Shape B has vertices at (−1,1), (−3,1), (−3,2). Describe fully the single transformation that maps A onto B. (3 marks)

Hint: Check each vertex. If x is negated and y stays same → reflection in y-axis. If both negate → rotation 180° about origin. State the transformation type, then all details needed.

+30 XP

3 marksEnlargement4MA1 style ✏️ No calculator

Triangle P has vertices at (2,1), (4,1), (4,3). It is enlarged with centre (0,0) and scale factor 2.5. Find the coordinates of the enlarged triangle. (3 marks)

Hint: For enlargement from origin: multiply each coordinate by the scale factor. For other centres: find the vector from centre to each vertex, multiply by SF, add back to centre.

+30 XP

4 marksVector proofGrade 7 Booklet style ✏️ No calculator

OABC is a parallelogram. OA = a and OC = c. M is the midpoint of BC. N is the midpoint of AB. Show that MN is parallel to OA. (4 marks)

Hint: Express the position vectors of M and N in terms of a and c. Find vector MN = ON − OM. If MN = k×(OA vector) for some scalar k, then MN is parallel to OA.

+40 XP

1 markColumn vector addition4MA1 style

Vector a = (3/−2) and vector b = (−1/5). What is 2a − b?

A (5/−1)

B (7/−9)

C (5/−9)

D (6/−4)

1 markScale factor negative4MA1 style

An enlargement with negative scale factor means:

A The image is smaller than the object

B The image is on the opposite side of the centre of enlargement, rotated 180°

C The image is reflected in the x-axis

D No transformation takes place

Transformations & Vectors

Transformations

Vectors

Module complete! 🎉