Question

If square ABCD is dilated by a scale factor of 1 3 with a dilation center at vertex A, by what factor does the area of the square decrease? A) 1 9 B) 1 2 C) 2 D) 4

Answer 1

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)