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