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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Translations as vectors worksheet — GCSE Foundation

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

MathsUKwww.geekhero.co.uk

1.A shape is translated by the vector $(3 - 8)$ , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector $(- 5 2)$ . Work out the coordinates of the image of that same vertex under this second translation.
(a)(7, 8)
(b)(11, 3)
(c)(3, 1)
(d)(11, −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 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.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)
5.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
6.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) $(- 7 4)$
7.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
8.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) $(- 3 - 5)$
9.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) $(- 3 - 8)$
10.A drone starts at the point (2, −3) on a coordinate grid. It flies by the vector $(4 6)$ and then by the vector $(- 9 - 1)$ . Write down the column vector that would take the drone straight back to its starting point.
(a) $(- 5 - 5)$
(b) $(5 - 5)$
(c) $(- 5 5)$
(d) $(- 13 - 7)$
11.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) $(4 0)$
12.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) $(5 6)$
13.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) $(- 6 - 5)$
14.A point is translated twice by the vector $(5 - 3)$ . Write down the single column vector that describes the overall translation.
(a) $(5 - 3)$
(b) $(10 - 6)$
(c) $(5 - 6)$
(d) $(15 - 9)$
15.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)

Build your own mix at the worksheet builder.