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.

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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.

Mathematics
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let's first draw `Isosceles trapezoid ABCD` |dw:1443240259301:dw|
|dw:1443240338434:dw|

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now let's have `line ZX drawn through its center` |dw:1443240353329:dw|
ah so the line is going through the center of the trapezoid vertically
it doesn't have to, but it's the easier ways to draw it I think
well the new trapezoid is 1/3 the original's size, but what about this new line's relation to line ZX?
what happens to A,B,C,D if we apply that scaling?
they should be the same proportionally right? but not the same length cause the shape has been dilated
it should be smaller, right? |dw:1443240673390:dw|
what do you notice about ZX and A'B'C'D' ?
line ZX cuts through the middle of A'B'C'D' just like ABCD, but is longer than the height of the new shape
it doesn't matter about the height the only thing that stays the same is that ZX still cuts through the center
actually I forgot to dilate Z and X they both move to their new points Z' and X' |dw:1443240926820:dw|
everything gets 1/3 closer to the center
So the new line Z'X' is simply 1/3 the original length of line ZX?
lines in geometry are infinitely long
if it were a line segment, then yes
ZX is a line segment though, right?
but they call it `line ZX`. They don't use segment at all
`what relationship will the new line have with line ZX?` they both go through the same center point (which is the dilation center point)
Man, its too late for me to do this type of school work. I can't think that well apparently. So that's the answer and I just have to explain that in complete sentences?
yeah exactly
alright thanks for the help then, its much appreciated
no problem

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