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anonymous

  • one year ago

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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  1. anonymous
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    let's first draw `Isosceles trapezoid ABCD` |dw:1443240259301:dw|

  3. jim_thompson5910
    • one year ago
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    |dw:1443240338434:dw|

  4. jim_thompson5910
    • one year ago
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    now let's have `line ZX drawn through its center` |dw:1443240353329:dw|

  5. anonymous
    • one year ago
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    ah so the line is going through the center of the trapezoid vertically

  6. jim_thompson5910
    • one year ago
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    it doesn't have to, but it's the easier ways to draw it I think

  7. anonymous
    • one year ago
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    well the new trapezoid is 1/3 the original's size, but what about this new line's relation to line ZX?

  8. jim_thompson5910
    • one year ago
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    what happens to A,B,C,D if we apply that scaling?

  9. anonymous
    • one year ago
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    they should be the same proportionally right? but not the same length cause the shape has been dilated

  10. jim_thompson5910
    • one year ago
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    it should be smaller, right? |dw:1443240673390:dw|

  11. jim_thompson5910
    • one year ago
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    what do you notice about ZX and A'B'C'D' ?

  12. anonymous
    • one year ago
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    line ZX cuts through the middle of A'B'C'D' just like ABCD, but is longer than the height of the new shape

  13. jim_thompson5910
    • one year ago
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    it doesn't matter about the height the only thing that stays the same is that ZX still cuts through the center

  14. jim_thompson5910
    • one year ago
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    actually I forgot to dilate Z and X they both move to their new points Z' and X' |dw:1443240926820:dw|

  15. jim_thompson5910
    • one year ago
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    everything gets 1/3 closer to the center

  16. anonymous
    • one year ago
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    So the new line Z'X' is simply 1/3 the original length of line ZX?

  17. jim_thompson5910
    • one year ago
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    lines in geometry are infinitely long

  18. jim_thompson5910
    • one year ago
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    if it were a line segment, then yes

  19. anonymous
    • one year ago
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    ZX is a line segment though, right?

  20. jim_thompson5910
    • one year ago
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    but they call it `line ZX`. They don't use segment at all

  21. jim_thompson5910
    • one year ago
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    `what relationship will the new line have with line ZX?` they both go through the same center point (which is the dilation center point)

  22. anonymous
    • one year ago
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    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?

  23. jim_thompson5910
    • one year ago
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    yeah exactly

  24. anonymous
    • one year ago
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    alright thanks for the help then, its much appreciated

  25. jim_thompson5910
    • one year ago
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    no problem

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