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 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.
- 2.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 3.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 4.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.
- 5.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
- 6.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.
- 7.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 8.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 9.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 10.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.
- 11.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.
- 12.Vector A is and vector B is . Write down how vector B compares to vector A.
- 13.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.
- 14.Write down the column vector, from the options given, that would move a point to the right and downwards.
- 15.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.
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