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 pin on a map is at grid reference (5, 2). It is moved by the vector . Write down its new grid reference.
- 2.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
- 3.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.
- 4.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.
- 5.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 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.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?
- 8.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.
- 9.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 10.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
- 11.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.
- 12.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 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 translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 15.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.
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