Let G be the center of equilateral triangle XYZ. A dilation centered at G with a 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 \(\frac{A}{[XYZ]}\).

So far all I have done is draw a diagram (one triangle facing up, another triangle facing down making it look like a star).

Any ideas on how to proceed after this? Which areas can I try and calculate to try and solve this problem?

xCorrosive Nov 4, 2020