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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 shape is translated by the vector $(- 7 4)$ and then by the vector $(3 - 9)$ . Write down the single column vector that has the same effect as those two translations together.
(a) $(- 4 - 5)$
(b) $(- 10 13)$
(c) $(- 4 - 13)$
(d) $(- 10 - 5)$
2.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)
3.Write down the column vector, from the options given, that would move a point to the right and downwards.
(a) $(3 - 4)$
(b) $(- 3 - 4)$
(c) $(- 3 4)$
(d) $(3 4)$
4.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) $(2 5)$
5.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.
(a) $(- 6 5)$
(b) $(6 5)$
(c) $(6 - 5)$
(d) $(- 6 - 5)$
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.
(a)(3, 8)
(b)(−5, 8)
(c)(0, −1)
(d)(−5, −4)
7.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) $(- 4 - 4)$
8.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) $(5 6)$
9.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
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 translation is described by the column vector $(- 2 7)$ . Write down a description of this translation in words, stating the horizontal and vertical movement.
(a)7 units left and 2 units up
(b)7 units right and 2 units down
(c)7 units right and 2 units up
(d)2 units right and 7 units down
12.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)
13.A shape is translated by the vector $(4 - 3)$ . The point P(6, 1) lies on the shape. Write down the coordinates of the image of P.
(a)(3, −3)
(b)(3, 5)
(c)(9, −3)
(d)(10, −2)
14.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) $(- 3 - 5)$
15.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) $(9 4)$

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