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 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.
- 2.Vector A is and vector B is . Write down how vector B compares to vector A.
- 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.The point R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 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.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.
- 7.A student says the reverse of the translation vector is . Write down the correct reverse translation vector.
- 8.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.
- 9.The column vector describes a translation. Write down the movement it represents.
- 10.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.
- 11.Write down the column vector, from the options given, that would move a point to the right and downwards.
- 12.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 13.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.
- 14.A pin on a map is at grid reference (5, 2). It is moved by the vector . Write down its new grid reference.
- 15.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.
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