A transformation of a figure in which all of the dimensions of the figure are multiplied by the same scale factor is called a dilation.
Effect of Dilation on Perimeter
Whenever a figure is dilated by a scale factor, the perimeter of the figure changes according to the same scale factor.
Effect of Dilation on Area
When a figure is dilated by a scale factor of [tex]\frac{a}{b}[/tex], the area of the figure is dilated by a scale factor of [tex]\frac{a^{2}}{b^{2}}[/tex]
Example-
Lets imagine a rectangle with length 10 cm and width 8 cm
So area becomes = 10*8 = 80 square cm
Lets suppose the rectangle is reduced by a scale factor of [tex]\frac{1}{2}[/tex] to produce a new rectangle.
So we will find the square of scale factor = [tex](\frac{1}{2})^{2}=\frac{1}{4}[/tex]
Now to find the area of the new rectangle(dilated one) we will multiply the area of the original rectangle by 1/4
= [tex]80*\frac{1}{4}=20[/tex]
Hence, area becomes 20 square cm.
