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Question
Find the image of point (4, -6) under the following operations:
(i) Mx . My (ii) My . Mx
(iii) MO . Mx (iv) Mx . MO
(v) MO . My (vi) My . MO
Write down a single transformation equivalent to each operation given above. State whether:
(a) MO . Mx = Mx . MO
(b) My . MO = MO . My
Solution
(i) Mx . My (4, -6) = Mx (-4, -6) = (-4, 6)
Single transformation equivalent to Mx . My is MO.
(ii) My . Mx (4, -6) = My (4, 6) = (-4, 6)
Single transformation equivalent to My . Mx is MO.
(iii) MO . Mx (4, -6) = MO (4, 6) = (-4, -6)
Single transformation equivalent to MO . Mx is My.
(iv) Mx . MO (4, -6) = Mx (-4, 6) = (-4, -6)
Single transformation equivalent to Mx . MO is My.
(v) MO . My (4, -6) = MO (-4, -6) = (4, 6)
Single transformation equivalent to MO . My is Mx.
(vi) My . MO (4, -6) = My (-4, 6) = (4, 6) Single transformation equivalent to Mx . MO is Mx.
From (iii) and (iv),
it is clear that MO . Mx = Mx . MO.
From (v) and (vi), it is clear that
My . MO = MO . My.
