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 (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.
- 2.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.
- 3.A shape is translated by the vector . The point P(6, 1) lies on the shape. Write down the coordinates of the image of P.
- 4.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 5.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 6.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?
- 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.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.
- 9.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.
- 10.The point R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 11.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
- 12.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 13.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.
- 14.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 15.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.
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