Transformations and vectors — IGCSE Mathematics (0580) questions by topic

On the grid, draw the image of triangle T after a rotation, 90 degrees clockwise, centre (0, 0).

m = (11, 5) [column vector with top component 11 and bottom component 5] n = (8, -3) [column vector with top component 8 and bottom component -3] Find 2m - n.

OABC is a rhombus and O is the origin. The diagonals of the rhombus intersect at P. Vector OP = 2m and vector AP = n. The diagram shows rhombus OABC with O at the bottom-left, A…

The grid shows triangle T with vertices at (-2, 1), (-2, 3), (-1, 1), and triangle U with vertices at (1, -1), (3, -1), (3, -2), drawn on an x-y grid from -4 to 4 on both axes.…

A is the point (3, -1). Vector AB = (2, -4) (column vector with top entry 2 and bottom entry -4). AC = 2 AB. Find the coordinates of the point C.

The diagram (NOT TO SCALE) shows a trapezium-like figure with points O, A, B, C and M. O is at the lower left, A is on the lower line to the right of O (vector OA = a). B is above…

The grid shows triangle A (small shaded triangle) and triangle B. Describe fully the single transformation that maps triangle A onto triangle B.

v = (2, −3) as a column vector (top component 2, bottom component −3). Find 5v.

Sue describes the single transformation that maps shape A onto shape B as a translation by the vector (7 over 1). Explain why Sue is incorrect.

Describe fully the single transformation that maps shape A onto shape B.

The diagram shows a quadrilateral OXPY with diagonals meeting at T (NOT TO SCALE). Y is top-left, P is top-right, O is bottom-left and X is bottom-right. The diagonals OP and XY…

a = (3, 7) and b = (−2, 5) (column vectors). Work out a − 2b.

F is the point (1, −4), FG = (8, −3) and GH = (−12, 35) (column vectors). Find 3FG.

The diagram shows three shapes A, B and C on a 1 cm² grid. Describe fully the single transformation that maps shape A onto shape B.

The grid shows triangles A, B and C. Describe the single transformation that maps triangle A onto triangle B.

Find the magnitude of the vector (−4, 5) (column vector).

F is the point (1, −4), FG = (8, −3) and GH = (−12, 35) (column vectors). Find 3FG.

The grid shows shapes A and B. Describe fully the single transformation that maps shape A onto shape B.

The grid shows triangles A and B. Describe fully the single transformation that maps triangle A onto triangle B.

The position vector of A is (5, 3) and BA = (4, 8) (column vectors). Show that OB = 5.1, correct to 1 decimal place.

a = (4, 9), b = (−6, 1), c = (13, −2) are column vectors. Work out a + b.

The diagram shows triangle ABC with angle ABC = 112° and angle ACB = 44°. M is the midpoint of AC. NOT TO SCALE. Triangle ABC is rotated 180° about centre M. The image and the…

The diagram shows a parallelogram OPQT. The position vector of P is a and the position vector of T is b. K is on PQ so that PK : KQ = 3 : 1. The lines OK and TQ are extended to…

The diagram shows triangle ABC with angle ABC = 112° and angle ACB = 44°. M is the midpoint of AC. NOT TO SCALE. Triangle ABC is rotated 180° about centre M. The image and the…

AB = (7, −3) is a column vector. Find 3·AB.

Triangles A, B and C are shown on the grid. Describe fully the single transformation that maps triangle A onto triangle B.

Triangles A, B and C are shown on the grid. Describe fully the single transformation that maps triangle A onto triangle B.

Shapes A, B and C are drawn on a grid. Describe fully the single transformation that maps shape A onto shape B.

ABC is a triangle. B is the point (1, −10), A is the point (4, 14) and CA = column vector (−11, 8). Find the coordinates of C.

Triangle T is drawn on a grid (vertices at (2, 3), (6, 3), (6, 5)). Translate triangle T by the vector (−7, 1). Label the image K.

O is the origin (0, 0), A is the point (8, 1) and B is the point (2, 5). NOT TO SCALE. Write OB as a column vector.

Triangles A and B are drawn on a grid. Describe fully the single transformation that maps triangle A onto triangle B.