Transformations

119.
In the diagram, A is the point (3, −2).
0 2 4 6 8 -2 2 4 6 8 A x y

Find the coordinates of the points B and C such that:
(a) B is the image of A after reflection in the line y = 2
(b) C is the image of A after translation by vector ( 2 6 )
(a) ......................... [2] (b) ......................... [2]
Paper 1
113.
The diagram shows four triangles A, B, C and D.
0 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -3 -2 -1 2 3 4 6 7 8 x y A B C D

(a) Describe fully the single transformation that maps

(i) A onto B,
............................................ [2]
(ii) C onto D.
.......................................... [3]
(b) Draw the image of triangle B after a rotation through 90° anticlockwise using the centre as (-1, 2).
[2]
Paper 3
114.
The diagram shows triangle A, B and C.
0 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -3 -2 -1 1 2 3 4 5 6 x y A B C

(a) Describe fully a single transformation which maps,

(i) A onto B,
......................................... [2]
(ii) A onto C.
......................................... [2]
(b) Draw the image of A after an enlargement, scale factor -1 2 and centre (0, 1).
Paper 3
115.
The diagram shows polygons D, G and H.
0 -10 -8 -6 -4 -2 2 4 6 8 10 -10 -8 -6 -4 -2 2 4 6 8 10 x y G D H

(a) Describe fully a single transformation that maps

(i) Polygon D onto polygon G,
............................................ [3]
(ii) Polygon D onto polygon H.
......................................... [2]
(b) On the grid, draw and label the image,

(i) R, of polygon G, after a reflection in the line x = 0,
[2]
(ii) M, of polygon D, after a rotation through 90° anti-clockwise about the point (-2,-2) .
[2]
Paper 3
116.
The line l, the point O and the quadrilateral ABCD and PQRS are shown on the grid.
l A B C D P Q R S O

(a) Write down the name of quadrilateral ABCD.
.................................................. [1]
(b) Describe a single transformation which maps ABCD onto PQRS.
..................................... [2]
(c) Reflect ABCD along line l.
[2]
(d) Rotate ABCD through 90° clockwise, centre A.
[3]
(e) Enlarge PQRS using scale factor 2, centre O.
[3]
Paper 3
117.
The diagram shows triangles A, B and C.
x y 0 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 A B C

(a) (i) Plot and label the point T (5,7) on the grid.
[3]
(ii) Rotate the point T through 90° clockwise about the origin. Label the image T'.
[2]
(b) Describe fully a single transformation that maps

(i) Triangle B onto triangle A,
................................. [2]
(ii) Triangle B onto triangle C.
.............................. [2]
(c) On the grid, draw the reflection of triangle B in the line y = 2.
[2]
Paper 3
118.
The diagram shows a line P, a kite ABCD and its image A'B'C'D'.
x y −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 A B C D A' B' C' D'

(a) Write down the coordinates of point C.
(......................... , .........................) [1]
(b) Given that point F (23, 22) is the image of A under translation, find the translation vector.
( ......................... ......................... ) [2]
(c) Draw the image of kite ABCD under reflection in the mirror line P.

Label the image A''B''C''D''.
[2]
(d) Describe fully a single transformation that maps kite ABCD onto A'B'C'D'.
..................................... [3]
(e) Draw the image of kite ABCD after enlargement using scale factor -2 and centre (-3,1) .

Label the image A'''B'''C'''D'''.
[2]
Paper 3
119.
The diagram shows triangles A, B and C on the grid.
x y −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 A B C

(a) Describe fully the single transformation that maps

(i) triangle A onto triangle B,
......................................... [3]
(ii) triangle A onto triangle C.
........................................... [3]
(b) On the grid,

(i) reflect triangle B in the line y = 2,
[2]
(ii) translate B by the vector ( -8 -10 )
[2]
Paper 3
120.
The diagram shows three trapezium A, B and C.
0 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 -2 -1 1 2 3 4 5 6 7 x y A B C

(a) Trapezium A is mapped onto trapezium D by translation ( 4 -2 ) .

Draw and label trapezium D.
(b) Describe fully the single transformation that maps

(i) B onto C,
........................................... [2]
(ii) A onto B.
......................................... [2]
(c) Trapezium C is mapped onto trapezium E by an enlargement, scale factor 2, centre (0,2) .

Draw and label trapezium E.
[2]
Paper 3