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# help!

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162
5

I have found two answers but they are incorecct for my two questions

1. Let G be the center of equilateral triangle XYZ. A dilation centered at G with scale factor $$-\frac{2}{3}$$is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find $$\frac{A}{[XYZ]}$$.

I found the answer 4/9 but the website i use said its not correct...

2. A square ABCD has an area of 4. The square is then dilated with a scale factor of x, producing a square A'B'C'D' of area 9. Find the sum of all possible values of x.

i found two answers 1.5 or -1.5 because the hint i was given was can scale factors be negative. I thought that there was only 1 answer 1.5 should i just add the two to get 0?

EDIT: The correct answer was 0! I wasnt thinking about the part where it said sum. It clicked once I wrote it out here.

Thank you so much!

Jul 22, 2020
edited by Guest  Jul 22, 2020

#3
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Important:::  If the value of scale factor k is negative, the dilation takes place in the opposite direction from the center of dilation on the same straight line containing the center and the pre-image point.

A / [xyz] = 0.407407407 = 11/27  Jul 23, 2020
edited by Dragan  Jul 23, 2020
edited by Dragan  Jul 23, 2020
#4
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OH wow thank you!! I understand now becuase of your note at the top so I can rember to use that in similar problems. Thank you so much!

Guest Jul 23, 2020
#5
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You're very welcome! Dragan  Jul 23, 2020