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.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
- 3.A courier drone delivers a parcel. It starts at the point (2, 1) on a map grid measured in kilometres. It flies by the vector to a warehouse, then by the vector to the delivery address. Work out the coordinates of the delivery address.
- 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.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 6.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
- 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.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 9.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 10.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.
- 11.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.
- 12.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 13.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.
- 14.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.
- 15.Vector A is and vector B is . Write down how vector B compares to vector A.
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