J20

(a) Triangle ABC with vertices A(2, 3), B(2, 6) and C(4, 3) onto triangle A1B1C1
with vertices at A1(6, 6), B1(6, 12) and C1(12, 6).
(b) Rectangle ABCD with vertices A(-3, -1), B(-3, -4), C(-1, -4),
D(-1, -1) onto rectangle A1B1C1D1 with vertices A1(-3, 1),
B1(-3, 4), C1(-1, 4) and D1(-1, 1).
(c)
Triangle PQR with vertices P(1, 1), Q(2, 4) and R(4, 1) onto triangle P1Q1R1
with vertices P1(0, 0), Q1(-4, 2) and R1(4, -2).
4. Use the points I and J to describe the transformation represented by each
Matrix.
(a)
0
1
2
0
(b)
1
0
0
2
(c)
0
1
2 0
(d)
1
0
0 2
5. Draw the triangle A(2, 2), B(6, 2), C(6, 4). Find its image under the
transformation represented by the following matrices:
(a)
(c)
0
1
0
1
1
0
1
0
(b)
(d)
1
0
0 1
1
0
2
1
0
2
6. Plot the object and image for the following:
(a)
2
0
Object: P(4, 2), Q(4, 4), R(0, 4); matrix:
0
2
(b)
0 1
Object: A(-6, 8), B(-2, 8), C(-2, 6); matrix:
1
0
Describe each as a single transformation.
7. Find and draw the image of the square (0. 0), (1, 1), (0, 2), (-1, 1) under the
transformation represented by the matrix
4 3
.
3 2
Show that the transformation is a shear and find the equation of the
invariant line.
8. Find and draw the image of the unit square O(0, 0), I(1, 0), K(1, 1) J(0, 1)
under the transformation represented by the matrix
3
0
. This transformation is called a two-way stretch.
0
2
Successive transformations