Matrix transformations

Triangle A and triangle B are drawn on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B

Triangle A is transformed to triangle C by a reflection in the line with equation y 1

On the grid, draw and label triangle C

Triangle A is transformed to triangle D by an enlargement with centre (0, 3) and scale factor 2

On the grid, draw and label triangle D

Triangle A is transformed to triangle E under the transformation with matrix M where

On the grid, draw and label triangle E

Turn over for a spare grid if you need to redraw your triangles.

Only use this grid if you need to redraw your triangles.

Triangles A and B are shown on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B

Triangle A is transformed to triangle C under the translation 81

On the grid, draw and label triangle C

Triangle A is transformed to triangle D under the transformation with the matrix M where

On the grid, draw and label triangle D

Triangle B is transformed to triangle E by a rotation of 180° about the point (0, 1)

On the grid, draw and label triangle E

Find the matrix which represents the transformation that maps triangle A onto triangle E

Turn over for a spare grid if you need to redraw your triangles.

Only use this grid if you need to redraw your triangles.

Triangle A and triangle B are drawn on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B

Triangle A is transformed to triangle C under an enlargement with scale factor 3 and centre of enlargement (6, 2)

On the grid, draw and label triangle C

Triangle A is transformed to triangle D under a reflection in the line with equation y = 3

On the grid, draw and label triangle D

Triangle B is transformed to triangle E under the transformation with matrix P where

Triangle E is transformed to triangle F under the transformation with matrix Q where

Triangle F is the image of triangle B under the matrix N

Given that the determinant of N is 2

find the coordinates of the vertices of triangle F

a b Determinant of matrix ad bc

Turn over for a spare grid if you need to redraw your triangles.

Only use this grid if you need to redraw your triangles.

Quadrilateral A is transformed to quadrilateral B under a reflection in the line y = − x

Quadrilateral C is the image of quadrilateral A under the matrix N

Find the matrix N

Trapeziums P and Q are drawn on the grid opposite.

Describe fully the single transformation that maps trapezium P onto trapezium Q

On the grid, draw and label trapezium A

Trapezium P is transformed to trapezium B by a rotation of 90° clockwise about the point (5, 2)

On the grid, draw and label trapezium B

Trapezium C is the image of trapezium Q under the transformation with matrix M where

On the grid, draw and label trapezium C

Turn over for a spare grid if you need to redraw your trapeziums.

Only use this grid if you need to redraw your trapeziums.

The determinant of matrix A is equal to the determinant of matrix B

Show that k is a root of the equation

Given that f(k) = 2k³ + 5k² – 28k – 15

use the factor theorem to show that (k + 5) is a factor of f(k)

Hence, factorise completely f(k)

The transformation with matrix C, where C is a 22 matrix, is equivalent to the transformation with matrix A followed by the transformation with matrix B

Given that k is positive,

find matrix C

The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.

On the grid, draw and label triangle A.

Triangle B is the image of triangle A under a reflection in the line with equation y = −x

On the grid, draw and label triangle B.

Triangle C is the image of triangle A under the transformation with the matrix M where

Hence, on the grid, draw and label triangle C.

Describe fully the single transformation that maps triangle B onto triangle C.

The single transformation that maps triangle B onto triangle C is represented by the matrix N

State, giving a reason, the matrix N²

Turn over for a spare grid if you need to redraw your triangles.

Only use this grid if you need to redraw your triangles.

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

On the grid opposite, draw and label triangle A.

Triangle B is the image of triangle A under the transformation with matrix M where

On the grid opposite, draw and label triangle B.

Triangle C is the image of triangle B under a reflection in the line with equation y = 0

On the grid opposite, draw and label triangle C.

Triangle A is transformed to triangle C under the transformation with matrix N.

Find matrix N.

Triangle D is the image of triangle C under a rotation through 180º about the point (1, 1)

On the grid opposite, draw and label triangle D.

Describe fully the single transformation that maps triangle D onto triangle A.

Turn over for a spare copy of the grid if you need to redraw your triangles.

Only use this grid if you need to redraw your triangles.

The vertices of triangle A are the points with coordinates (0, 0), (1, 0) and (0, 2)

On the grid opposite, draw and label triangle A.

Triangle A is transformed to triangle B under the transformation with matrix M where

On the grid, draw and label triangle B.

The transformation with matrix M is equivalent to an enlargement with centre the origin, with scale factor k followed by an anticlockwise rotation of θ ° about the origin.

Calculate the value of k.

Calculate the value, to one decimal place, of θ.

Triangle B is transformed to triangle C under a reflection in the x‑axis.

On the grid, draw and label triangle C.

Triangle A is transformed to triangle C under the transformation with matrix T.

Find matrix T.

Turn over for a spare grid if you need to redraw your triangles.

Only use this grid if you need to redraw your triangles.