Evaluate the composite transformation matrix, Mechanical Engineering

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A triangle ABC with vertices A (30,20), B(90,20), C(30,80) is to be scaled by a factor of 0.5 about a point X(50,40). Calculate :-

(i) The composite transformation matrix; and

(ii) The coordinates of the vertices for a scaled triangle.

A rectangle ABCD has vertices A(1,1), B(2,1), C(2,3) and D(3,2). It is to be rotated by 30 in clockwise direction about point P(3,2). Evaluate :

(i) The composite transformation matrix; and

(ii) the new coordinates of rectangle.

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