J20

9. Draw triangle XYZ with X(1, 2), Y(1, 5) and Z(2, 5).
(a) Draw the image of triangle XYZ under the transformation represented by
0
1
the matrix and label it X1Y1Z1.
1
0
(b) Describe this transformation.
(c) Draw the image of triangle XYZ under a half-turn about the origin and label
it X2Y2Z2.
(d) Find the matrix which represents this transformation.
(e) Describe the single transformation that maps triangle X1Y1Z1 onto X2Y2Z2.
(f) Find the matrix which represents this transformation.
10. On a squared paper draw a triangle with its vertices at (3, -1), (5, -1) and
(5, -4) and label it L.
(a) Triangle L is mapped onto triangle L1 under an anticlockwise rotation of 90 0
about the origin. Draw L1 in the same plane.
(b) Triangle L is mapped onto triangle L2 under a transformation represented by
1
0
M = . Draw L2 in the same plane.
0
1
(c) Triangle L3 has vertices (-3, -1), (-7, -1) and (-7, 5). Draw L3 in the same
plane.
(d) Describe fully the single transformation that maps triangle L onto L3.
11. Draw triangle R whose vertices are (1, 1), (1, 3) and (5, 3). Triangle S is the image
of triangle R under the transformation represented by
1
2
M = .
0
1
(a) Calculate the area of triangle R.
(b) Describe fully the single transformation that is represented by matrix M.
(c) Find M -1 .
(d) What is the image of triangle R under the transformation represented by M -1 ?
12. Draw and label a triangle whose vertices are A(1, 4), B(2, 4) and C(2, 1).
(a) Enlargement E with centre at the origin maps triangle ABC onto triangle
A 1B 1C 1. Given that the coordinates of A 1 are (4, 16):
(i) draw and label triangle A 1B 1C 1.
(ii) state the scale factor of E.
(b) Point B 2(-4, -2) is the image of B under a reflection in line L. Find the
equation of L.
(c) R is a clockwise rotation of 90 0 about the origin and it maps triangle ABC
onto triangle A 3B 3C 3.
(i) Draw and label triangle A 3B 3C 3.
(ii) Find the matrix representing R.
3 0
(d) Transformation S is represented by the matrix and maps triangle
0 1
ABC onto triangle A 4B 4C 4.