Let G be the center of equilateral triangle XYZ A dilation centered at G with scale factor -1 is applied to triangle XYZ to obtain triangle X'Y'Z' Let A be the area of the region that is contained inside both triangles XYZ and X'Y'Z' Find A/[XYZ]

parmen Jun 19, 2024

#1**0 **

A dilation of -1 means the points X, Y, and Z are just reflected over point G to create points X', Y', and Z'. Assume D is where line YG meets XZ. G is the centroid of the triangle, so the ratio of YG to GD is 2:1. Now, you just do some length chasing (I'm sorry I'm dumb to find a way to prove it) to figure out that triangle XYZ can be expressed as 9 congruent equilateral triangles and 6 of those triangles form the regular hexagon known as region A. Therefore, the ratio of A/[XYZ] would be 6/9=2/3

P.S. Tell me if I did anything wrong! :D

P.P.S. CPhill or the other people would be much better at explaining this

P.P.P.S. Plz tell me how to use latex in this website thx

Tottenham10 Jun 19, 2024