Composition of Two Consecutive Rotations are Equal

Note the image above, A' is a point A shadow by rotation as far as α clock direction with center P and A" is the shadow of point A' by rotation as far as β clockwise with center P also. it appears that the mapping from A to A" is (α + β) is clockwise with center P. Thus we can draw the conclusion:

Two consecutive rotations are equal to a rotation as far as the number of each of the original rotais of the same center.

Example:
A(-2, 6) is rotated as far as 65° clockwise with center O followed by a clockwise rotation of 70° with center O as well. Determine the point A shadow!

Answer:
a = -65° (clockwise)
B = -70°(clockwise)
a + B = -65° + (-70°)
a + b = -135°

The matrix of the above rotation composition is:

Specifying the shadow A is as follows:

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Referensi :

• To'Ali's book math group accounting and sales

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