J20
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Stretches<br />
Properties of a stretch<br />
(a)<br />
(b)<br />
(c)<br />
Example<br />
The direction of the stretch is perpendicular to the invariant line.<br />
The scale factor is given by<br />
distanceof the imagepointfrom the invariantline<br />
distanceof the objectpointfrom the invariantline<br />
Points on the opposite sides of the invariant line move in opposite directions but<br />
perpendicular to the invariant line.<br />
The square OABC is stretched, parallel to the X-axis, to become the rectangle<br />
O A′ B′<br />
C′<br />
Such that O A′<br />
= 4 × OA<br />
Transformation matrices<br />
Matrices can be used to represent transformations. In the x-y plane, we use<br />
2×2 matrices to represent transformations. The matrices can be determined by<br />
the use of the identity matrix or calculations.<br />
The identity matrix<br />
Consider the unit square OIKJ with coordinates O(0, 0), I(1, 0), K(1, 1) and<br />
1<br />
0<br />
J(0, 1). When the position vectors I = and J = are written in matrix form,<br />
0<br />
1<br />
<br />
1<br />
0<br />
they give the identity matrix I = . In this matrix, the first column is the<br />
0<br />
1<br />
position vector of I and the second column is the position vector of J.
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