Transformations - Worksheets, Questions and Revision

22 original exam-style questions - 16 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Geometry and Measures

3.17 Transformations

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Triangle A has vertices at (-5, 4), (-5, 1) and (-3, 1). Triangle A is translated by the vector (5, -2) to give triangle B.
x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 0 A
(Total for Question 1 is 2 marks)
2
Rectangle P has vertices at (2, 1), (5, 1), (5, 3) and (2, 3). Rectangle P is reflected in the x-axis to give rectangle Q.
x y O -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 P
(Total for Question 2 is 2 marks)
3
Which one of these transformations does NOT always give an image that is congruent to the original shape?
  • A) Translation
  • B) Reflection
  • C) Rotation
  • D) Enlargement with scale factor 3
(Total for Question 3 is 1 mark)
4
Shape A has vertices at (-6, -5), (-6, -3), (-4, -3) and (-4, -5). Shape B has vertices at (-1, 0), (-1, 2), (1, 2) and (1, 0).
x y O -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 A B
(Total for Question 4 is 2 marks)
5
Triangle C has vertices at (1, 2), (1, 5) and (3, 2). Triangle C is reflected in the y-axis to give triangle C'.
x y O -6 -4 -2 2 4 6 -6 -4 -2 2 4 6 C
(Total for Question 5 is 2 marks)
6
Quadrilateral D has vertices at (1, 1), (4, 1), (4, 2) and (1, 3). Quadrilateral D is reflected in the line y = x to give quadrilateral D'.
x y -4 -2 2 4 -4 -2 2 4 y = x D
(Total for Question 6 is 2 marks)
7
Triangle E has vertices at (2, 1), (5, 1) and (2, 4). Triangle E is rotated 90 degrees clockwise about the origin O to give triangle E'.
x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 O E
(Total for Question 7 is 3 marks)
8
Shape F has vertices at (2, 2), (4, 2) and (4, 3). Shape F is rotated 180 degrees about the point (1, 1) to give shape F'.
x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 O F
(Total for Question 8 is 3 marks)
9
Shape P has vertices at (1, 1), (1, 3) and (3, 1). Shape Q has vertices at (1, -1), (1, -3) and (3, -1).
x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 0 P Q
(Total for Question 9 is 2 marks)
10
Shape R has vertices at (2, 3), (2, 6) and (4, 3). Shape S has vertices at (-3, 2), (-6, 2) and (-3, 4).
x y -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 0 R S
(Total for Question 10 is 3 marks)
11
Triangle T has vertices at (1, 1), (2, 1) and (1, 2). Triangle T is enlarged by scale factor 3, centre (0, 0), to give triangle T'.
-1 1 2 3 4 5 6 7 -1 1 2 3 4 5 6 7 O T
(Total for Question 11 is 3 marks)
12
Shape U has vertices at (1, 1), (3, 1) and (1, 3). Shape V has vertices at (1, 1), (5, 1) and (1, 5).
-1 0 1 2 3 4 5 6 7 -1 1 2 3 4 5 6 7 x y U V
(Total for Question 12 is 3 marks)
13
A model of a bridge is made using a scale of 1 : 250. The length of the model bridge is 60 cm.
(a)Work out the real length of the bridge. Give your answer in metres.(2)
(b)The real bridge is enlarged in a scale drawing so that 1 cm on the drawing represents 5 m. Work out the length of the bridge on this scale drawing. Give your answer in centimetres.(2)
(Total for Question 13 is 4 marks)
14
Point A has coordinates (-2, 5). Point A is translated by the vector (-3, -6) to give point B.
(Total for Question 14 is 2 marks)
15
Triangle A has a vertex at (-4, 3). After a translation, the corresponding vertex on triangle B is at (1, -2). Which vector describes this translation?
  • A) (5, -5)
  • B) (-5, 5)
  • C) (5, 5)
  • D) (-3, 1)
(Total for Question 15 is 1 mark)
16
Point (4, -2) is rotated 90 degrees anticlockwise about the origin.
  • A) (2, 4)
  • B) (-2, -4)
  • C) (2, -4)
  • D) (-2, 4)
(Total for Question 16 is 1 mark)
17
A model train is built using a scale of 1 : 76. The length of a real carriage is 19 metres.
(Total for Question 17 is 3 marks)
18
Triangle W has vertices at (2, 4), (6, 4) and (2, 8). Triangle W is enlarged by scale factor 1/2, centre (0, 0), to give triangle W'.
x y -1 1 2 3 4 5 6 7 8 9 -1 1 2 3 4 5 6 7 8 9 O W
(Total for Question 18 is 3 marks)
19
Shape X has vertices at (-2, 5), (2, 5) and (-2, 3). Shape Y has vertices at (0, 4), (2, 4) and (0, 3).
-4 -3 -2 -1 1 2 3 4 5 6 -4 -3 -2 -1 1 2 3 4 5 6 0 x y X Y
(Total for Question 19 is 3 marks)
20
Triangle A has vertices at (1, 1), (3, 1) and (1, 3).
x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 A
(a)Triangle A is reflected in the x-axis to give triangle B. Find the coordinates of the vertices of triangle B.(2)
(b)Triangle B is then translated by the vector (-2, 4) to give triangle C. Find the coordinates of the vertices of triangle C.(2)
(Total for Question 20 is 4 marks)
21
Triangle D has vertices at (1, 1), (3, 1) and (1, 2). Triangle D is enlarged by scale factor -1, centre (0, 0), to give triangle D'.
x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 O D
(Total for Question 21 is 3 marks)
22
Triangle E is reflected in the x-axis, and the image is then reflected in the y-axis, to give triangle F.
(Total for Question 22 is 3 marks)
Mark scheme · 3.17 Transformations

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22