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

• 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:
  \( (x’, y’) = (x \cdot k, y \cdot k) \)

Examples

Practice Questions:

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 \(L'(0,0.25)\)