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 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.
- 2.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.
- 3.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.
- 4.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.
- 5.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 6.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 7.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 8.Write down the column vector, from the options given, that would move a point to the right and downwards.
- 9.Vector A is and vector B is . Write down how vector B compares to vector A.
- 10.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
- 11.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 12.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.
- 13.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.
- 14.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 15.A shape is translated by the vector , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector . Work out the coordinates of the image of that same vertex under this second translation.
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