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A 2D geometric shape is rotated about a point with coordinates (1,2) by 90° in a clockwise direction. Then, the shape is scaled about the same point in the x-coordinate by 2 times and in the y-coordinate by 3 times. Finally, the shape is reflected about the origin. Derive the single combined transformation matrix for these operations.
Answer: The sequence of transformations is as follows.
From right to left the sequence is as follows- (i) Translate so that (1,2) moves to origin (ii) Rotate about the origin by -90° (iii) Scale by (2,3) (iv) Translate back so that (1,2) is at its previous position (v) Flip about the origin. Single combined transformation can be obtained by multiplying all these matrices.
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