When a rectangle is dilated, how do the perimeter and area of the rectangle change?

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 , the area of the figure is  dilated by a scale factor of

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 to produce a new rectangle.

So we will find the square of scale factor =

Now to find the area of the new rectangle(dilated one) we will multiply the area of the original rectangle by 1/4

=

Hence, area becomes 20 square cm.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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