Assuming you meant to say "scale factor 1/3", then the answer is A) 1/9
This is because we simply square the scale factor to get
(1/3)^2 = (1/3)*(1/3) = 1/9
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For example, let's say we had a square that was 18 by 18. Its area would be 18*18 = 324 square units.
Now reduce each side by the scale factor 1/3 getting the new length 18*(1/3) = 6. The new area is 6*6 = 36
Compare 36 and 324 to see that 36/324 = 1/9. The new area is 1/9th of the old one
new area = (1/9)*(old area)
The factor by which the area of the square ABCD is decrease when it is dilated by a scale factor of 1/3 is 1/9.
Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.
The area of square is the square of its sides length. It can be given as,
[tex]A=a^2[/tex]
Here, (a) is the length of the side of the square.
The square ABCD is dilated by a scale factor of 1/3. The center of dilation is at vertex A.
By this dilation the area is shrinked and the area of the dilated square will be decrease. The scale factor by which area decrease is,
[tex]k=\left(\dfrac{1}{3}\right)^2\\k=\dfrac{1}{9}[/tex]
Hence, the factor by which the area of the square ABCD is decrease when it is dilated by a scale factor of 1/3 is 1/9.
Learn more about the dilation of the figure here;
https://brainly.com/question/3457976
