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 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.
- 2.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 3.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.
- 4.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 5.Write down the column vector, from the options given, that would move a point to the right and downwards.
- 6.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.
- 7.A courier drone delivers a parcel. It starts at the point (2, 1) on a map grid measured in kilometres. It flies by the vector to a warehouse, then by the vector to the delivery address. Work out the coordinates of the delivery address.
- 8.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.
- 9.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.
- 10.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.
- 11.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 12.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 13.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.
- 14.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 15.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
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