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.
(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.
(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).
(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'.
(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'.
(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'.
(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'.
(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).
(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).
(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'.
(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).
(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'.
(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).
(Total for Question 19 is 3 marks)
20
Triangle A has vertices at (1, 1), (3, 1) and (1, 3).
(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'.
(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
M1 adds 5 to each x-coordinate and subtracts 2 from each y-coordinate (oe), at least one correct vertex shown
A1 all three vertices correct: (0,2), (0,-1), (2,-1) cao
Answer: (0, 2), (0, -1), (2, -1)
Question 2
M1 y-coordinates negated, x-coordinates unchanged (oe), at least one correct vertex shown
A1 all four vertices correct: (2,-1), (5,-1), (5,-3), (2,-3) cao
Answer: (2, -1), (5, -1), (5, -3), (2, -3)
Question 3
B1 D oe
Answer: D) Enlargement with scale factor 3
Question 4
B1 translation (oe 'translated')
B1 vector (5, 5) oe, may be written as a column vector
Answer: Translation by vector (5, 5)
Question 5
M1 x-coordinates negated, y-coordinates unchanged (oe), at least one correct vertex shown
A1 all three vertices correct: (-1,2), (-1,5), (-3,2) cao
Answer: (-1, 2), (-1, 5), (-3, 2)
Question 6
M1 x and y coordinates swapped (oe), at least two correct vertices shown
A1 all four vertices correct: (1,1), (1,4), (2,4), (3,1) cao
Answer: (1, 1), (1, 4), (2, 4), (3, 1)
Question 7
M1 applies the rule (x,y) -> (y,-x) oe to at least one vertex
A1 at least two vertices correct
A1 all three vertices correct: (1,-2), (1,-5), (4,-2) cao
Answer: (1, -2), (1, -5), (4, -2)
Question 8
M1 applies the rule (x,y) -> (2-x, 2-y) oe to at least one vertex
A1 at least two vertices correct
A1 all three vertices correct: (0,0), (-2,0), (-2,-1) cao