Find the image of point (4, -6) under the following operations :

(i) $M_{x} . M_{y}$ (ii) $M_{y} . M_{x}$

(iii) $M_{o} . M_{x}$ (iv) $M_{x} . M_{o}$

(v) $M_{o} . M_{y}$ (vi) $M_{y} . M_{o}$

Write down a single transformation equivalent to each operation given above.

State whether :

(a) $M_{o} . M_{x}$ = $M_{x} . M_{o}$

(b) $M_{y} . M_{o}$ = $M_{o} . M_{y}$

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Solution

(i) M_x . M_y(4, -6) = M_x (-4, -6) = (-4, 6)
Single transformation equivalent to M_x . M_y is M_O.
(ii) M_y . M_x(4, -6) = M_y (4, 6) = (-4, 6)
Single transformation equivalent to M_y . M_x is M_O.
(iii) M_O . M_x(4, -6) = M_O (4, 6) = (-4, -6)
Single transformation equivalent to M_O . M_x is M_y.
(iv) M_x . M_O(4, -6) = M_x (-4, 6) = (-4, -6)
Single transformation equivalent to M_x . M_O is M_y.
(v) M_O . M_y(4, -6) = M_O (-4, -6) = (4, 6)
Single transformation equivalent to M_O . M_y is M_x.
(vi) M_y . M_O(4, -6) = M_y (-4, 6) = (4, 6)

Single transformation equivalent to My . M_O is M_x.
From (iii) and (iv), it is clear that M_O . M_x = M_x . M_O.
From (v) and (vi), it is clear that M_y . M_O = M_O . M_y.

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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