Refer to the following diagram. In position 1, a 10-metre rod is placed 10 metres from a fixed point, P. Six small discs, A to F, are evenly spaced along the length of the rod. The rod is rotated anti-clockwise about its centre by α = 30° to position 2. The distances from P to the discs are denoted by x.

a. What effect does the 30° rotation have on values of x? Investigate this by first considering the effect on the average distance from P to the discs.

b. Find two values that can be used as measures of the change in the variation of x caused by the rotation.

c. Use the values obtained in parts a and b to summarise the changes in the distances from P to the discs caused by the rotation.

d. Can you prove that Σ­x² is constant for all values of 0° < α < 90°?

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Position 1 Position 2 maaUni 10 10 D P C 10 E Revi F E F