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.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.
- 2.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.
- 3.The point R(−6, 9) is translated by the vector . Write down the coordinates of the image of R.
- 4.A pin on a map is at grid reference (5, 2). It is moved by the vector . Write down its new grid reference.
- 5.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.
- 6.The vector describes a translation. A student writes it as by mistake. Write down what error the student has made.
- 7.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
- 8.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
- 9.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?
- 10.A translation is described by the column vector . Write down the column vector of the translation that undoes it.
- 11.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.
- 12.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.
- 13.A translation is described by the column vector . Write down a description of this translation in words, stating the horizontal and vertical movement.
- 14.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.
- 15.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.
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