Printable · GCSE Foundation · ages 14-16
Translations as vectors worksheet — GCSE Foundation
Fifteen questions on "translations as vectors" — DfE statement G24. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Translations as vectors worksheet — GCSE Foundation
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- 1.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 2.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 3.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 4.The point R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 5.A shape is translated by the vector and then by the vector . Write down the single column vector that has the same effect as those two translations together.
- 6.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 7.A robotic arm's tip starts at the point (12.5, −4.25) on a grid measured in centimetres. It moves by the vector to pick up a component, then by the vector to place it. Work out the coordinates of the tip after both moves.
- 8.A shape is translated by the vector , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector . Work out the coordinates of the image of that same vertex under this second translation.
- 9.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.
- 10.A shape is translated by the vector . The point P(6, 1) lies on the shape. Write down the coordinates of the image of P.
- 11.Quadrilateral ABCD has vertices A(1, 1), B(5, 1), C(5, 4) and D(1, 4). The quadrilateral is translated by the vector . Which of these points is NOT a vertex of the image?
- 12.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 13.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
- 14.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.
- 15.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
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