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 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.
- 2.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 3.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.
- 4.The point M(3, 8) is translated by the vector . Write down the coordinates of the image of M.
- 5.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.
- 6.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.
- 7.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.
- 8.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.
- 9.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 10.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 11.The point R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 12.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.
- 13.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
- 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.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.
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