J20

(c)
Find the areas of rectangles ABCD and A1B1C1D1.
3. A rectangle has vertices (1, 1), 1, 3), (4, 1) and (4, 3). Find the area of its image
under the transformation represented by each of the following matrices.
(a)
1
0
2
1
(b)
0
4
3
3
(c)
4
0
1
0
1
(d)
2
8
0 1
3
0
4. Under a transformation represented by matrix N = , rectangle A1B1C1D1 with
0
2
vertices at A1(6, 2), B1(6, 6), C1(15, 6) and D1(15, 2), is the image of rectangle
ABCD.
(a) Determine the area of rectangle ABCD.
(b) Find the coordinates of A, B, C and D.
1
2
5. The matrix represents a transformation R.
0
1
(a) Find the images of the following points under R.
(i) (1, 2) (ii) (-1, -1).
(b) Describe transformation R fully.
6. Points A(-5, 1), B(-1, -1) and C(2, 5) are three vertices of rectangle ABCD.
(a) Determine the coordinates of D.
(b) Describe fully a single transformation (not a reflection) that maps A onto D,
and B onto C.
7. Triangle T has vertices (2, 1), (4, 1) and (3, 3).
(a) Find the area of the triangle.
(b) Find the area of the image of T when it is transformed under the matrix:
0
1
2
2
(i)
(ii)
1
0
1
3
3
4
6
0
(iii)
(iv)
1
3
1 .
4
3
8. Triangle K, whose vertices are P(2, 3), Q(5, 3) and R(4, 1), is mapped onto triangle
K1 whose vertices are P1(-4, 3), Q1(-1, 3) and R1(x, y) by a transformation given by
a
b
matrix M = .
c
d
(a) Find the:
(i) elements of matrix M
(ii) coordinates of R1.
(b) Triangle K2 is the image of triangle K1 under a reflection in the line y = x.
Find a single matrix that maps K onto K2.