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.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.
- 2.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.
- 3.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.
- 4.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 5.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.
- 6.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.
- 7.Vector A is and vector B is . Write down how vector B compares to vector A.
- 8.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.
- 9.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 10.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 11.The point R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 12.A pin on a map is at grid reference (5, 2). It is moved by the vector . Write down its new grid reference.
- 13.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 14.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.
- 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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