J20
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(a)<br />
3<br />
0 0<br />
1<br />
<br />
0<br />
2<br />
0<br />
0<br />
1 0<br />
0<br />
3 3 0 <br />
= . Therefore, the image has vertices at:<br />
1 1<br />
0<br />
0 2 2<br />
O(0, 0), I1(3, 0), K1(3, 2) and J1(0, 2).<br />
(b) The determinant of N is (3 × 2) – (0 × 0) = 6.<br />
(c) The area of OI1K1J1 = 3 × 2 = 6 square units.<br />
The area of the unit square is 1 square unit.<br />
The area of the image is 6 square units. From this information we have<br />
the area of the image<br />
the areaof the object is the same as the determinant of the transformation matrix.<br />
Exercise<br />
1. Find the area of the image of the unit square under the transformations<br />
represented by each of the following matrices.<br />
(a)<br />
2<br />
0<br />
2<br />
6<br />
<br />
(b) <br />
0<br />
2<br />
1<br />
5<br />
(c)<br />
5<br />
1 <br />
1<br />
3<br />
<br />
(d) <br />
0<br />
4<br />
0<br />
1<br />
(e)<br />
3<br />
0<br />
1<br />
0<br />
<br />
(f) <br />
0<br />
1 <br />
0 1<br />
(g)<br />
4<br />
6<br />
<br />
<br />
1<br />
3<br />
2 (h) 3<br />
2<br />
<br />
.<br />
<br />
6<br />
4<br />
2. A rectangle with vertices at A(0, 0), B(4, 0), C(4, 3) and D(0, 3) is<br />
1 2<br />
transformed under the matrix .<br />
1<br />
4<br />
(a) Find the coordinates of the vertices of the image, A1B1C1D1.<br />
(b) Draw rectangle ABCD and its image on the same axes.
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