Translation

The point A is at (2, 5). It is translated by the vector (3, −2), that is 3 to the right and 2 down.

Write down the coordinates of the image of A.

The point P is at (−1, 4). It is translated by the vector (−3, −5), that is 3 to the left and 5 down.

Write down the coordinates of the image of P.

Rhys says that a translation by the vector (3, −2) moves a shape 3 to the left and 2 up.

Rhys is wrong. Describe the movement correctly.

A point A at (3, 2) is translated to A′ at (8, −1).

Write down the vector of the translation, in the form (a, b).

A triangle has vertices at (2, 3), (5, 3) and (2, 7).

The triangle is translated by the vector (4, −2), that is 4 units to the right and 2 units down.

Write down the coordinates of the vertices of the image.

Triangle B is a translation of triangle A.

Write down the vector of the translation that maps triangle A onto triangle B.

Triangle P has vertices at (1, 1), (4, 1) and (1, 3). It is translated by the vector (−2, 3) to give triangle Q.

1. Write down the coordinates of the vertices of triangle Q.
2. Write down the vector that translates triangle Q back to triangle P.

Square ABCD has vertices A (0, 0), B (2, 0), C (2, 2) and D (0, 2). The square is translated so that the image of A is at (−3, 4).

1. Write down the vector of the translation.
2. Work out the coordinates of the image of C.

Triangle A has vertices at (1, 1), (3, 1) and (1, 4).

Triangle B has vertices at (5, −1), (7, −1) and (5, 2).

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

Triangle P is reflected in the line L₁ (x = 2) to give triangle Q.

Triangle Q is then reflected in the line L₂ (x = 5) to give triangle R.

1. On the grid, draw triangle Q and triangle R.
2. Describe the single transformation that maps triangle P onto triangle R.

A shape is translated by the vector (2, 3) and then by the vector (−5, 1).

1. Write down the single vector that gives the same translation.
2. Write down the vector that moves the shape back to its starting position.

Triangle A has vertices at (2, 1), (5, 1) and (2, 3).

Triangle A is reflected in the y-axis to give triangle B.

1. Write down the coordinates of the vertices of triangle B.
2. Triangle C has vertices at (−1, −2), (−4, −2) and (−1, 0). Find the vector of the translation that maps triangle B onto triangle C.

Triangle T is rotated 180° about the origin O to give triangle T₁.

Triangle T₁ is then translated by the vector (4, 0) to give triangle T₂.

1. On the grid, draw triangle T₁ and triangle T₂.
2. Describe fully the single transformation that maps triangle T onto triangle T₂.