How to Perform Similarity Transformations: Step-by-Step Guide

A similarity transformation combines rigid motions with a dilation, so it preserves shape but not size. Two figures are similar exactly when such a sequence maps one onto the other.

• Center of Dilation: A fixed point in the plane.
• Scale Factor: The ratio by which a figure is enlarged or reduced. A scale factor greater than (1) results in an enlargement, while a scale factor between (0) and (1) results in a reduction. The formula for dilation from a center point ((x, y)) with a scale factor (k) is:
  ( (x’, y’) = (x cdot k, y cdot k) )

Worked examples: similarity transformations

Practice questions on similarity transformations

1. A square has vertices at (E(3,4)), (F(6,4)), (G(6,7)), and (H(3,7)). What are the vertices of the square after a dilation with a scale factor of (3), centered at the origin?
2. A rhombus has vertices at (I(-2,3)), (J(2,5)), (K(4,3)), and (L(0,1)). Determine the vertices of the rhombus after a dilation with a scale factor of (0.25), centered at the origin.

1. (E'(9,12)), (F'(18,12)), (G'(18,21)), and (H'(9,21))
2. (I'(-0.5,0.75)), (J'(0.5,1.25)), (K'(1,0.75)), and (L'(0,0.25))

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