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.
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.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.
- 3.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 4.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.
- 5.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 6.The column vector describes a translation. Write down the movement it represents.
- 7.A pin on a map is at grid reference (5, 2). It is moved by the vector . Write down its new grid reference.
- 8.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 9.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.
- 10.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 11.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.
- 12.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 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 point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
- 15.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.
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