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- When it is rotated by \(180°\), \(270°\) and \(360°\) also the structure looks the same.
- Hence, when the windmill takes one complete turn, there are four positions at which the structure looks the same.
- Therefore because of this, we say it has rotational symmetry of order 4.
Figure 2(i) is the original position of the cross. If it is rotated by \(90°\) about the centre \(O\), we get figure 2(ii). Now observe the position of the cross. Rotate the cross again by \(90°\), and you get figure 2(iii). When the cross completes four quarter-turns, the cross reaches its original position Figure 2(v), which is similar to Figure 2(i). You can check the coordinates of the cross after each turn and note the number of turns the cross is taking to come to its original position.
Thus, We can see the cross (ABCD) has rotational symmetry of order 4 about its centre \(O\).
(i) The centre of rotation is the centre of the cross marked as \(O\).
(ii) The angle of rotation is \(90°\).
(iii) The direction of rotation is clockwise.
(iv) The order of rotational symmetry is \(4\).
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