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.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.
- 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 point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 4.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 5.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.
- 6.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
- 7.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.
- 8.A pin on a map is at grid reference (5, 2). It is moved by the vector . Write down its new grid reference.
- 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.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.
- 11.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 12.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 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.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 15.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.
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