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. 


Please help with number 1!

Thank you so much!

 Jul 22, 2020
edited by Guest  Jul 22, 2020

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  laugh


 Jul 23, 2020
edited by Dragan  Jul 23, 2020
edited by Dragan  Jul 23, 2020

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

You're very welcome!smiley

Dragan  Jul 23, 2020

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