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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

Maths · GCSE Foundation · G24 · Translations as vectors · 15 questions

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1.A pin on a map is at grid reference (5, 2). It is moved by the vector $(4 - 3)$ . Write down its new grid reference.
(a)(2, 6)
(b)(8, 6)
(c)(9, −1)
(d)(2, 2)
2.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
(a) $(4 4)$
(b) $(4 - 4)$
(c) $(- 4 4)$
(d) $(- 4 - 4)$
3.The point R(−6, 9) is translated by the vector $(- 11 5)$ . Write down the coordinates of the image of R.
(a)(−1, 9)
(b)(−1, −2)
(c)(−6, −2)
(d)(−11, 20)
4.Vector A is $(- 5 2)$ and vector B is $(5 - 2)$ . Write down how vector B compares to vector A.
(a)B is the same as A
(b)B is unrelated to A in direction
(c)B is twice A
(d)B is the reverse of A
5.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.
(a)(3, 8)
(b)(−5, 8)
(c)(0, −1)
(d)(−5, −4)
6.A student says the reverse of the translation vector $(- 9 4)$ is $(9 4)$ . Write down the correct reverse translation vector.
(a) $(- 9 - 4)$
(b) $(- 9 4)$
(c) $(9 - 4)$
(d) $(9 4)$
7.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector $(- 9 6)$ 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.
(a) $(- 2 8)$
(b) $(- 7 - 2)$
(c) $(7 2)$
(d) $(- 7 4)$
8.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.
(a) $(2 - 5)$
(b) $(8 9)$
(c) $(- 2 5)$
(d) $(2 5)$
9.The vector $(- 2 5)$ describes a translation. A student writes it as $(5 - 2)$ by mistake. Write down what error the student has made.
(a)Doubled the x component
(b)Reversed both signs
(c)Swapped the x and y components
(d)Reversed only the y sign
10.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.
(a) $(8 3)$
(b) $(3 8)$
(c) $(5 10)$
(d) $(- 3 - 8)$
11.A robotic arm's tip starts at the point (12.5, −4.25) on a grid measured in centimetres. It moves by the vector $(6.5 - 3.75)$ to pick up a component, then by the vector $(- 1.5 2.25)$ to place it. Work out the coordinates of the tip after both moves.
(a)(0.75, 11)
(b)(8.75, 2.25)
(c)(6.5, 3.75)
(d)(11, 0.75)
12.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.
(a)(−18, 23)
(b)(22, −13)
(c)(2, 5)
(d)(12, −4)
13.The column vector $(2 - 6)$ describes a translation. Write down the movement it represents.
(a)6 left, 2 up
(b)6 left, 2 down
(c)2 left, 6 up
(d)6 right, 2 up
14.A translation is described by the column vector $(- 5 6)$ . Write down the column vector of the translation that undoes it.
(a) $(6 - 5)$
(b) $(- 5 - 6)$
(c) $(5 - 6)$
(d) $(5 6)$
15.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
(a) $(- 5 - 3)$
(b) $(- 3 5)$
(c) $(3 - 5)$
(d) $(- 3 - 5)$

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