IGCSE Maths Transformations & vectors topical questions

Each rule maps (x, y) to an image point.

1. (a)Describe the transformation (x, y) → (x + 5, y − 3).[1]
2. (b)Describe the transformation (x, y) → (−x, y).[1]
3. (c)Describe the transformation (x, y) → (y, x).[2]

Rotate about the origin.

1. (a)Find the image of (3, 2) after a 180° rotation about O.[2]
2. (b)Find the image of (3, 2) after a 90° clockwise rotation about O.[2]

A quadrilateral has vertices A(1, 1), B(4, 1), C(4, 3) and D(1, 3).

1. (a)The quadrilateral is reflected in the x-axis. Write down the coordinates of the four image vertices.[3]
2. (b)Write down the translation vector that maps A to C.[2]

The point P(6, −2) is rotated through 90° clockwise about O to P₁, then reflected in the x-axis to P₂.

1. (a)Find the coordinates of P₁.[2]
2. (b)Find the coordinates of P₂.[2]
3. (c)Describe the single transformation that maps P straight to P₂.[1]

A triangle has vertices (0, 0), (2, 0) and (0, 4), and area 4 cm². It is enlarged by scale factor 3, centre O.

1. (a)Write down the coordinates of the image vertices.[2]
2. (b)Write down the area scale factor.[2]
3. (c)State the area of the image triangle.[1]

A triangle has vertices (1, 2), (3, 2) and (1, 5). It is enlarged by scale factor −2, centre O. (Extended)

1. (a)Find the coordinates of the image vertices.[3]
2. (b)Describe the position of the image relative to the original.[2]

a = (4, −2) and b = (−1, 5). (Extended)

1. (a)Find a + b.[1]
2. (b)Find 2a − b.[2]
3. (c)Find |a|, giving your answer in surd form.[2]

A(−2, 3) and B(4, 11). (Extended)

1. (a)Write AB as a column vector.[2]
2. (b)Find |AB|.[2]

A triangle with vertices (1, 1), (5, 1) and (1, 4) has area 6 cm². It is enlarged by scale factor −2, centre O. (Extended)

1. (a)Find the coordinates of the three image vertices.[3]
2. (b)Find the area of the image triangle.[2]

a = (1, 2) and b = (3, 3). (Extended)

1. (a)Find 3a + 2b as a column vector.[2]
2. (b)Find the magnitude of 3a + 2b.[2]
3. (c)Find the vector c such that a + b + c = 0.[2]

u = (2, 5), v = (6, 15) and w = (4, 8). (Extended)

1. (a)Show that u and v are parallel.[2]
2. (b)Explain why w is not parallel to u.[1]
3. (c)Find the scalar t such that t·u = (−8, −20).[2]

OACB is a parallelogram with OA = a and OC = c. M is the midpoint of OA. (Extended)

1. (a)Express AC in terms of a and c.[2]
2. (b)Express MC in terms of a and c.[2]
3. (c)Given a = (4, 0) and c = (6, 2), write MC as a column vector.[2]

OAB is a triangle with OA = a and OB = b. M is the midpoint of AB and G lies on OM with OG = ⅔ OM. (Extended)

1. (a)Find AB in terms of a and b.[1]
2. (b)Find OM in terms of a and b.[2]
3. (c)Show that AG = ⅓b − ⅔a.[3]

Rectangle K(1, 1), L(4, 1), M(4, 3), N(1, 3) has area 6 cm². It is enlarged by scale factor −1 about the point (2, 2). (Extended)

1. (a)Find the coordinates of the four image vertices.[3]
2. (b)Describe the single transformation with the same effect.[2]
3. (c)Write down the area of the image.[1]