anonymous
  • anonymous
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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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
let's first draw `Isosceles trapezoid ABCD` |dw:1443240259301:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1443240338434:dw|

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More answers

jim_thompson5910
  • jim_thompson5910
now let's have `line ZX drawn through its center` |dw:1443240353329:dw|
anonymous
  • anonymous
ah so the line is going through the center of the trapezoid vertically
jim_thompson5910
  • jim_thompson5910
it doesn't have to, but it's the easier ways to draw it I think
anonymous
  • anonymous
well the new trapezoid is 1/3 the original's size, but what about this new line's relation to line ZX?
jim_thompson5910
  • jim_thompson5910
what happens to A,B,C,D if we apply that scaling?
anonymous
  • anonymous
they should be the same proportionally right? but not the same length cause the shape has been dilated
jim_thompson5910
  • jim_thompson5910
it should be smaller, right? |dw:1443240673390:dw|
jim_thompson5910
  • jim_thompson5910
what do you notice about ZX and A'B'C'D' ?
anonymous
  • anonymous
line ZX cuts through the middle of A'B'C'D' just like ABCD, but is longer than the height of the new shape
jim_thompson5910
  • jim_thompson5910
it doesn't matter about the height the only thing that stays the same is that ZX still cuts through the center
jim_thompson5910
  • jim_thompson5910
actually I forgot to dilate Z and X they both move to their new points Z' and X' |dw:1443240926820:dw|
jim_thompson5910
  • jim_thompson5910
everything gets 1/3 closer to the center
anonymous
  • anonymous
So the new line Z'X' is simply 1/3 the original length of line ZX?
jim_thompson5910
  • jim_thompson5910
lines in geometry are infinitely long
jim_thompson5910
  • jim_thompson5910
if it were a line segment, then yes
anonymous
  • anonymous
ZX is a line segment though, right?
jim_thompson5910
  • jim_thompson5910
but they call it `line ZX`. They don't use segment at all
jim_thompson5910
  • jim_thompson5910
`what relationship will the new line have with line ZX?` they both go through the same center point (which is the dilation center point)
anonymous
  • anonymous
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?
jim_thompson5910
  • jim_thompson5910
yeah exactly
anonymous
  • anonymous
alright thanks for the help then, its much appreciated
jim_thompson5910
  • jim_thompson5910
no problem

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