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.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.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 R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 4.The column vector describes a translation. Write down the movement it represents.
- 5.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 6.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.
- 7.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.
- 8.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 9.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 10.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.
- 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.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 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.
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