Dilation (Scale Factor)

Dilation is a transformation that alters the size of a figure but not its shape. It involves a center of dilation and a scale factor.

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Each dimension of the triangle is multiplied by 2, making the triangle twice as large.

The algebraic representation is @@(x, y) ightarrow igg(rac{1}{2}x, rac{1}{2}yigg)@@.

The scale factor can be determined by dividing the length of a side of the dilated figure by the corresponding side of the original figure.

The center of dilation is a fixed point in the plane about which all points of a figure are expanded or contracted.

The sides of triangle A'B'C' are three times the length of the corresponding sides of triangle ABC.

The new coordinates will be (3x, 3y).

The area of the dilated quadrilateral A'B'C'D' will be 1/9 of the area of quadrilateral ABCD.

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.