Dilation
Transformation in a plane characterized by a fixed point C, called the centre of dilation, and a real number k, called the scale factor, such that, regardless of the points P and Q not equal to C, the ratio of the algebraic measure of the directed line segment D(PQ) to the algebraic measure of the directed line segment PQ is equal to k.
Symbols
- The symbol generally used to refer to a dilation is the letter D.
- The centre C of the dilation can be denoted by "[latex]D_{c}[/latex]"
Properties
- When a dilation has only one fixed point, the point is called the "centre C of the dilation."
- A dilation enlarges a figure if |k|> 1 and reduces a figure if 0 < |k| < 1.
- The image of a figure transformed by a dilation is a figure that is similar to the initial figure.
- A dilation with a scale factor k equal to 1 is a dilation that transforms a figure onto itself. This is an identity transformation.
- the centre of a dilation, which is a fixed point;
- the lines that map the dilation
- the length ratio between a segment and its image;
- parallelism;
- the measures of angles;
- the orientation of the plane.
Examples
This is a positive dilation (or a dilation with a positive scale factor):.svg)
This is a negative dilation (or a dilation with a negative scale factor):
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