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 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.
- 2.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 3.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 4.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 5.Write down the column vector, from the options given, that would move a point to the right and downwards.
- 6.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.
- 7.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.
- 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 is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 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.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 12.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 13.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.
- 14.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.
- 15.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?
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