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.
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Translations as vectors worksheet — GCSE Foundation
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- 1.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.
- 2.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 3.A crane's hook starts at the point (3.4, 9.5) on a construction site plan measured in metres. It moves along the vector to pick up a beam, then along the vector to place it. Work out the single column vector that describes the hook's overall movement from its start position to where it places the beam.
- 4.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.
- 5.A robot on a grid moves by the vector , then by the vector , then by the vector . Write down the single column vector that has the same overall effect as these three moves.
- 6.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 7.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 8.A drone starts at the point (3.5, −2) on a grid measured in metres. It flies by the vector to check a first sensor. The drone then needs to fly in a straight line to reach the point (−1.7, 9) to check a second sensor. Work out the column vector of this second flight.
- 9.A drone starts at the point (2, −3) on a coordinate grid. It flies by the vector and then by the vector . Write down the column vector that would take the drone straight back to its starting point.
- 10.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 11.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.
- 12.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 13.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 14.The point R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 15.The column vector describes a translation. Write down the movement it represents.
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