Transformation
1. A is the point (1, 7) B is the point (6, 7)
The line AB is mapped onto the line PQ by the translation
(a) Find the coordinates of Q
(b) What special type of quadrilateral is ABQP?
(c) Find the area of the quadrilateral ABQP.
2.
3. Triangles A, B, C and D are drawn on a centimetre square
grid
(a) The perimeter of triangle A is (a+√b) cm, where a and b
are integers. Find a and b.
(b) Triangle A is mapped onto triangle B by the translation
T. Write down the column vector that represents T.
(c) Describe fully the single transformation that maps
triangle B onto triangle C.
(d) Describe fully the single transformation that maps
triangle B onto triangle D.
(e) Write down the matrix that represents the
transformation which maps triangle D onto triangle A.
(f) The transformation V is a reflection in the line y = 0. The transformation W is a rotation 90° clockwise about
(0, 0). The single transformation X is equivalent to the transformation V followed by the transformation W.
(i) The point (g, h) is mapped onto the point P by the transformation X. Find the coordinates of P
(ii) Describe fully the single transformation X.
4.
5. The diagram shows triangles A, B and C
(i) Describe fully the single transformation that maps
triangle A onto triangle B
(ii) Describe fully the single transformation that maps
triangle A onto triangle C.
(iii) Another transformation is
represented by the matrix P, where This
transformation maps triangle A onto
triangle D. Find the vertices of triangle D
(iv) Describe fully the single
transformation represented by the
matrix P
6. (a) The diagram shows triangles A, B
and C
(i) Describe fully the single
transformation that maps
(a) triangle A onto triangle B,
(b) triangle A onto triangle C.
(ii) One vertex of triangle A is (2, 1).
Find the coordinates of this point
when it is
(a) reflected in the line y = –x
(b) rotated through 90°
anticlockwise about (1, –1).
(b) You may use the grid below to help you answer this question. The points (2, 1), (4, 3), (3, 1) and (p, q) form a
quadrilateral. This quadrilateral has rotational symmetry order 1 and one line of symmetry.
(i) One possible position of (p, q) is (2, 2). Write down the name of this special quadrilateral.
(ii) Given that p and q are integers, find two other possible positions of (p, q)
7. Shapes A and B are drawn on the grid.
(a) Draw the image of shape A after a translation
with vector .
(b) Draw the image of shape A after an enlargement with
scale factor and cen-1/2 centre (1, 0).
(c) Shape A is mapped onto shape B by the single
transformation P.
(i) Describe fully the transformation P.
(ii) Find the matrix representing transformation P.
8. The diagram shows triangle A and line L.
(i) Triangle A is mapped onto triangle B by a reflection in
line L. Draw and label triangle B. [2]
(ii) Triangle A is mapped onto triangle C by an
anticlockwise rotation of 90°, centre (0, 3). Draw and label
triangle C. [2]
(iii) Triangle C is mapped onto triangle D by a reflection in
line L. Describe the single transformation that maps
triangle B onto triangle D
9. The points (2, 3), (4, 3) and (4, 4) are the vertices of a
triangle A. (use a grid -10 ≤ x ≤ 5 and -5 ≤ y ≤ 10
(a) On the grid, draw and label triangle A.(1)
(b) Triangle A is transformed to triangle B under the translation On the grid, draw and label triangle B.(1)
(c) Triangle B is transformed to triangle C under the transformation with matrix T where Find the coordinates of
the vertices of triangle C.(2)
(d) On the grid, draw and label triangle C.(1)
(e) Triangle B is mapped to triangle C under the transformation with matrix T by an anticlockwise rotation about
the origin of 180° followed by an enlargement with centre the origin. Find the scale factor of this
enlargement.(1)
(f) Triangle C is transformed to triangle D under the translation On the grid, draw and label triangle D.(1)
(g) Triangle A is transformed to triangle D by a single enlargement. Describe fully this enlargement.
10. (a)
(b)
11. Triangle A is drawn on the grid.
(a) Transformation P is represented
by the matrix P maps triangle A
onto triangle B.
(i) Draw and label triangle B.
(ii) Describe fully the single transformation P.
(iii) Write down the ratio area of triangle A : area
of triangle B.
(b) Transformation Q is represented
by the matrix Q maps triangle B onto
triangle C. Draw and label triangle C.
(c) Transformation Y is represented by
the matrix Y maps triangle A onto
triangle D. Find the matrix that
represents the transformation that maps triangle
D onto triangle A.
