Isosceles trapezoid ABCD is constructed with line ZX drawn through its center. If the isosceles trapezoid is dilated using a scale factor of one over three and a line is drawn through the center of the new dilated figure, what relationship will the new line have with line ZX? Explain your reasoning using complete sentences.

Question

Vocaloid · Answer

my best guess would be that the new line is also (1/3) of the old line, I just need to think of a good geometric proof

woolyfrog · Answer

ok

Vocaloid · Answer

@563blackghost I'm a little occupied right now can you take a look ;_;

woolyfrog · Answer

u there blackghost? lol

563blackghost · Answer

yea XD

I would say that Vocaloid is right. Since the trapezoid is dilated by 1/3 then the trapezoid would be similar to the original one...only dilated not disformed...so the lengths of the trapezoid would follow by this 1/3 of a scale factor. This means the lengths of both trapezoids would be proportional. So the relationship between segment zx and the line would be similar but zx is scaled by a factor of 1/3 to create the new line.