Combined transformations

Shape S is rotated 90° clockwise about (0, 0) and the image is then rotated 180° about (0, 0).

Describe fully the single transformation that maps S onto its final image.

Triangle A has vertices (1, 1), (3, 1) and (1, 2).

Triangle A is rotated 90° clockwise about (0, 0) to give triangle B.

Triangle B is then translated by the vector (2, 3) to give triangle C.

Write down the coordinates of the vertices of triangle C.

Triangle T has vertices (1, 2), (4, 2) and (1, 4).

T is translated by the vector (−3, −1) and the image is then reflected in the y-axis.

Write down the coordinates of the vertices of the final image.

Triangle T has vertices at (1, 1), (3, 1) and (1, 2).

Triangle T is reflected in the y-axis to give triangle T₁.

Triangle T₁ is then reflected in the x-axis to give triangle T₂.

Describe fully the single transformation that maps triangle T onto triangle T₂.

Shape P is reflected in the line x = 3. The image is then reflected in the line y = 2.

1. Write down the coordinates of the one point that is not moved by either reflection.
2. Describe fully the single transformation that maps P onto its final image.

Triangle P is reflected in the line x = 2 to give triangle Q.

Triangle Q is reflected in the line x = 5 to give triangle R.

Describe fully the single transformation that maps P onto R.

Triangle A has vertices at (2, 2), (4, 2) and (2, 6).

Triangle B has vertices at (1, 1), (2, 1) and (1, 3).

Triangle C has vertices at (−1, 1), (−2, 1) and (−1, 3).

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

Triangle A has vertices at (2, 2), (6, 2) and (6, 4).

1. Triangle A is enlarged by scale factor −12, centre (0, 0), to give triangle B. Write down the coordinates of the vertices of triangle B.
2. Describe fully the single transformation that maps triangle B back onto triangle A.

Triangle S has vertices (1, 1), (2, 1) and (2, 3).

1. S is reflected in the x-axis and the image is then enlarged by scale factor 2, centre (0, 0). Work out the final position of each vertex. Then show that enlarging first and reflecting second gives the same final image.
2. The point (1, 1) is translated by the vector (1, 0) and then enlarged by scale factor 2, centre (0, 0). Show that enlarging first and translating second gives a different point, so the order can matter.

A shape is rotated 180° about (0, 0) and the image is then translated by the vector (4, 2).

The two steps together are the same as a single rotation of 180°.

Find the coordinates of the centre of this single rotation.