J20

0
Column represents I
1
(the image of I).
1
1
Column represents J 1 (the image of J)
0
Draw I, J, I 1 and J 1 on a diagram. Clearly both I and J have been rotated 90 0 clockwise
about the origin.
0 1
represents a rotation of -90 0 about the origin.
1
0
This method can be used to describe a reflection, rotation, enlargement, shear or stretch
in which the origin remains fixed.
Exercise
1. Triangle XYZ has vertices X(1, 1), Y(2, 4) and Z(4, 4). Determine the matrix which
represents each of the following transformations and hence the coordinates of the
vertices of the image triangle X 1 Y 1 Z 1 .
(a) Reflection in the x-axis
(b)
(c)
(d)
(e)
Reflection in the y-axis.
A rotation of -90 0 about the origin.
A rotation of 90 0 about the origin.
A half turn about the origin.
(f) An enlargement of scale factor -2 with centre O.
2. Determine the matrix that can transform each of the following pairs of points onto
their respective images.
(a) A(1, 2) and B(3, 0) onto A1(4, 4) and B1(3, 9).
(b) A(-2, 1) and B(5, -3) onto A1(1, -2) and B1(1(-3, 5)
(c) M(4, 5) and N(-1, 6) onto M1(-4, 5) and N1(1, 6)
(d)
P(8, 3) and Q(0, 5) onto P1(8, 3) and Q1(0,5)
3. Determine the matrix that can transform each of the following shapes onto their
corresponding images.