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

Maths · GCSE Foundation · G24 · Translations as vectors · Non-calculator · 15 questions

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1.Quadrilateral ABCD has vertices A(1, 1), B(5, 1), C(5, 4) and D(1, 4). The quadrilateral is translated by the vector $(3 - 2)$ . Which of these points is NOT a vertex of the image?
(a)(−1, 1)
(b)(3, 4)
(c)(−1, 4)
(d)(3, 7)
2.A courier drone delivers a parcel. It starts at the point (2, 1) on a map grid measured in kilometres. It flies by the vector $(- 3 5)$ to a warehouse, then by the vector $(4 - 1)$ to the delivery address. Work out the coordinates of the delivery address.
(a)(7, −2)
(b)(11, −3)
(c)(8, −6)
(d)(6, 2)
3.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) $(2 5)$
4.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
5.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) $(- 3 - 8)$
6.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) $(5 6)$
7.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
8.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)
9.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)
10.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)
11.After a translation by the vector $(6 - 2)$ , a point lands on (4, 1). Write down the coordinates of the point before the translation.
(a)(2, −5)
(b)(2, 7)
(c)(6, −5)
(d)(6, 7)
12.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
13.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)
14.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) $(3 4)$
15.A robot on a grid moves by the vector $(- 2 3)$ , then by the vector $(5 - 7)$ , then by the vector $(1 4)$ . Write down the single column vector that has the same overall effect as these three moves.
(a) $(- 6 14)$
(b) $(0 4)$
(c) $(3 - 4)$
(d) $(4 0)$

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