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OpenSessame Group Title

Find the image of P(–2, –1) after two reflections; first Ry=-5 and then Rx=1. A. (–2, –1) B. (–1, –6) C. (4, –9) D. (1, –5)

  • one year ago
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  1. e.mccormick Group Title
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    So the Ry=-5 and Rx=1 are the lines you need to reflect across?

    • one year ago
  2. OpenSessame Group Title
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    Those are the reflections

    • one year ago
  3. e.mccormick Group Title
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    A reflection is usually over a line.... so I want to make sure that is the notation you are using.

    • one year ago
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    I think so...

    • one year ago
  5. e.mccormick Group Title
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    http://www.mathopenref.com/reflect.html Like it says there, "A transformation where each point in a shape appears at an equal distance on the opposite side of a given line - the line of reflection. " So, start by just doing a rough sketch. Does not need to be exact, but you need to find where the dot and line would be and how far the line is from the dot. If you can do that with math, great! But a sketch can help.

    • one year ago
  6. OpenSessame Group Title
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    Okay, but i dont understand what i have to do...

    • one year ago
  7. e.mccormick Group Title
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    Well, it needs to be an equal distance from the line on the other side of the line.

    • one year ago
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    Where did the line come from????

    • one year ago
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    You lost me..

    • one year ago
  10. e.mccormick Group Title
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    Ry=-5 \(\leftarrow\) that is the line part.

    • one year ago
  11. e.mccormick Group Title
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    Let me show you an example.

    • one year ago
  12. OpenSessame Group Title
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    Okay...Just show me with this one

    • one year ago
  13. e.mccormick Group Title
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    If I work this that is me giving you an answer. If I work an example you can follow the process and answer your own homework. Lets say I take this random dot: |dw:1376455485961:dw| And lets say I have Ry=1, so the line where every Y is 1.

    • one year ago
  14. e.mccormick Group Title
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    |dw:1376455572591:dw|

    • one year ago
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    Well, im really lost man...So i wouldnt even get it

    • one year ago
  16. OpenSessame Group Title
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    That is an example already, im just doing a text review for before i take it. so it doesnt count

    • one year ago
  17. e.mccormick Group Title
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    The important measure is the distance from the dot to the line. |dw:1376455620753:dw| Because I need to put the reflection the SAME DISTANCE on the other side of the line.

    • one year ago
  18. e.mccormick Group Title
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    |dw:1376455677255:dw|

    • one year ago
  19. OpenSessame Group Title
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    Do the distance is the number in the equation?

    • one year ago
  20. OpenSessame Group Title
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    Let me try to do mine...one sec

    • one year ago
  21. e.mccormick Group Title
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    The distance is the measure from your point and the line.

    • one year ago
  22. e.mccormick Group Title
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    Yours is done twice.... so see what you get for the first step and I can check it. Then the second step.

    • one year ago
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    |dw:1376455841757:dw|

    • one year ago
  24. e.mccormick Group Title
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    OK, that is a good (-2,-1).

    • one year ago
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    |dw:1376455914360:dw|

    • one year ago
  26. OpenSessame Group Title
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    Now what do i do exactly?

    • one year ago
  27. e.mccormick Group Title
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    OK, so what is the measure of the distance between your dot and the line? |dw:1376456012468:dw|

    • one year ago
  28. OpenSessame Group Title
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    -3?

    • one year ago
  29. e.mccormick Group Title
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    Not quite. Tewo problems. This is change in y, not x, and distance is always positive.

    • one year ago
  30. OpenSessame Group Title
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    so 4?

    • one year ago
  31. e.mccormick Group Title
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    Yes. So your point is 4 above the line. That means the reflection must be 4 BELOW the line!

    • one year ago
  32. OpenSessame Group Title
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    so at -5?

    • one year ago
  33. OpenSessame Group Title
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    wait no....-4?

    • one year ago
  34. e.mccormick Group Title
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    The line is at -5. So 4 below -5.... or -5-4=?

    • one year ago
  35. e.mccormick Group Title
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    Above is +, below is -. Similarly, to the left of is -, to the right of is +. Has to do with the Cartesian (xy) plane rules.

    • one year ago
  36. OpenSessame Group Title
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    Ohhhh so -9?

    • one year ago
  37. e.mccormick Group Title
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    Yes. That means the X is the same and the Y is now -9. So, the point after 1 translation is at (-2,-9). |dw:1376456612998:dw|

    • one year ago
  38. e.mccormick Group Title
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    Now you have the line Rx=1 to do the second reflection over.

    • one year ago
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    okay:) i get it!

    • one year ago
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    |dw:1376456678313:dw|

    • one year ago
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    |dw:1376456695550:dw|

    • one year ago
  42. e.mccormick Group Title
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    So, how far this time?

    • one year ago
  43. OpenSessame Group Title
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    3?

    • one year ago
  44. e.mccormick Group Title
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    \(\large\ddot\smile\)

    • one year ago
  45. OpenSessame Group Title
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    so the point would me three to the right?

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  46. OpenSessame Group Title
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    so (4,-9)????

    • one year ago
  47. e.mccormick Group Title
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    Yes, 3 to the right of 1. And yep, that is it. (4,-9).

    • one year ago
  48. OpenSessame Group Title
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    wait im gonna see if it matches...

    • one year ago
  49. e.mccormick Group Title
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    Now, once you get good at the math, you should not need a sketch, but if yuou are ever in doubt, the rough sketch is there to help!

    • one year ago
  50. OpenSessame Group Title
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    Okay, the textbook just didnt really explain it

    • one year ago
  51. e.mccormick Group Title
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    The thing I think most people mes up here is the line.... because x=0 is the y axis, and y=0 is the x axis. So they give you a y line but you draw it the same way as the x axis and that can be confusing!

    • one year ago
  52. OpenSessame Group Title
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    yea, thats the right answer! thanks:)

    • one year ago
  53. OpenSessame Group Title
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    Can you help with some other questions that i dont get?

    • one year ago
  54. e.mccormick Group Title
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    Probably. I can explain it the same basic way I always do and hopefully it works like this and you get it!

    • one year ago
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    Okay, thanks:)

    • one year ago
  56. OpenSessame Group Title
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    What composition of rigid motions and a dilation maps EFGH to the dashed figure? https://study.ashworthcollege.edu/access/content/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_9_files/mc020-1.jpg

    • one year ago
  57. e.mccormick Group Title
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    OK. Dilation is going to be the size change. The rigit motion will get it from one place to the other.

    • one year ago
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    Okay...

    • one year ago
  59. e.mccormick Group Title
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    It is probably easiest to do the dilation first. That will be some multiplication number. It is a ratio of the sides.

    • one year ago
  60. OpenSessame Group Title
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    Okay...

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  61. e.mccormick Group Title
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    For example, this would be a dialation by 3..... |dw:1376457753408:dw| So start by finding how long the sides of both rectangles are.

    • one year ago
  62. OpenSessame Group Title
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    wait is the answer D2*T<0,-6>

    • one year ago
  63. e.mccormick Group Title
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    2x the size, so yah, a dialation of 2. I didn't do the rest yet, but that would probably do it.

    • one year ago
  64. OpenSessame Group Title
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    Really??? woooohoooo

    • one year ago
  65. e.mccormick Group Title
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    Hmmm.... -6.... is that enough on the translation?

    • one year ago
  66. OpenSessame Group Title
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    Idk...

    • one year ago
  67. e.mccormick Group Title
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    Well, lets look at this real quick: |dw:1376458028692:dw| Now you need to double the size.

    • one year ago
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    The dialation is times 2?

    • one year ago
  69. e.mccormick Group Title
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    |dw:1376458060944:dw| OK, that makes them reflections of each other.

    • one year ago
  70. e.mccormick Group Title
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    So now, one of two things needs to happne.... It either needs to be reflected over the x axis, OR, corner H needs to go all the way down to the bottom corner. |dw:1376458143764:dw|

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  71. OpenSessame Group Title
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    so its shifted down -6

    • one year ago
  72. e.mccormick Group Title
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    Well, is that 6? That bottom corner is at -9....

    • one year ago
  73. OpenSessame Group Title
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    -10?

    • one year ago
  74. e.mccormick Group Title
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    or -10, actually.... counted wrong.

    • one year ago
  75. e.mccormick Group Title
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    So it has to go from 2 above to -10 below... so....

    • one year ago
  76. OpenSessame Group Title
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    so uhm...It would be 11?

    • one year ago
  77. OpenSessame Group Title
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    12

    • one year ago
  78. e.mccormick Group Title
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    Yep! So 2D, T\(\langle 0,-12\rangle\) is more like it.

    • one year ago
  79. OpenSessame Group Title
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    that isnt one of my options

    • one year ago
  80. e.mccormick Group Title
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    Hmmm.... AH.... OK... the dialaion is probably also changing the translation! \(2\langle 0,-6\rangle = \langle 0,-12\rangle\)

    • one year ago
  81. e.mccormick Group Title
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    So my bad. Looks like you did have it right.

    • one year ago
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    YUS:) thanks though!

    • one year ago
  83. OpenSessame Group Title
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    The hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles. What is r(240drg,0)(G)

    • one year ago
  84. e.mccormick Group Title
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    Well, the good news is you should understand the why a bit better! By exploring these, it lets you understand the why of it all....

    • one year ago
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    okay!

    • one year ago
  86. e.mccormick Group Title
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    Hmmm..... I have not seen that form of question.... my geometry was a while back, and they have changed some of the things they do... Do you know what it is looking for, any terms? An angle?

    • one year ago
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    240 degrees

    • one year ago
  88. OpenSessame Group Title
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    Thats really all i understand...

    • one year ago
  89. e.mccormick Group Title
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    r is usually a radius.... but there is no distance....

    • one year ago
  90. OpenSessame Group Title
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    I think r is the point?

    • one year ago
  91. e.mccormick Group Title
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    Is it R and not r?

    • one year ago
  92. OpenSessame Group Title
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    Thats the problem..

    • one year ago
  93. e.mccormick Group Title
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    hmmm..... Well, 240/30=8 segments.

    • one year ago
  94. OpenSessame Group Title
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    so 8 to the left or right?

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  95. e.mccormick Group Title
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    Well, if r is right... but that would be a guess on my part. Right 8 of G? I would need to see the reference to know they type of peoblem to get this one.

    • one year ago
  96. OpenSessame Group Title
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    So would it be K???

    • one year ago
  97. e.mccormick Group Title
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    I would only be guessing without the book and chapter.

    • one year ago
  98. OpenSessame Group Title
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    Okay...Well for me thats better then nothing!

    • one year ago
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    The vertices of a triangle are P(–8, 6), Q(1, –3), and R(–6, –3). Name the vertices of \[R _{y=x}(PQR)\]

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  100. e.mccormick Group Title
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    Is that a reflection over the y axis?

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  101. OpenSessame Group Title
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    I believe it is.

    • one year ago
  102. e.mccormick Group Title
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    AH HA! Found a reference! http://www.regentsprep.org/Regents/math/geometry/GT6/composition.htm

    • one year ago
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    You did??

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  104. OpenSessame Group Title
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    OOOOO

    • one year ago
  105. e.mccormick Group Title
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    The composition part does not matter here.... the \(R_y\) part is reflection over the y axis!

    • one year ago
  106. OpenSessame Group Title
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    So just make it the other sign?

    • one year ago
  107. e.mccormick Group Title
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    And even better! http://www.regentsprep.org/Regents/math/geometry/GT5/reviewTranformations.htm

    • one year ago
  108. OpenSessame Group Title
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    Would the first point be (-6,8)

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  109. OpenSessame Group Title
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    OHHHH!!! MAKES SENSE!

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  110. OpenSessame Group Title
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    so (6,-8)

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  111. e.mccormick Group Title
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    Amazing what finding a reference to the symbols can do!

    • one year ago
  112. OpenSessame Group Title
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    YEA! Thanks so much man!

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  113. OpenSessame Group Title
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    Write a sequence of rigid motions that maps ab and xy

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  114. OpenSessame Group Title
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    LAST ONE AND I WILL UNDERSTAND GEOMETRY!

    • one year ago
  115. e.mccormick Group Title
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    That composition part also confirms what we talked about with the <0,-6> becoming <0,-12>. The SECOND part of the compositon happens first!

    • one year ago
  116. OpenSessame Group Title
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    the second part is (AB=XY)

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  117. e.mccormick Group Title
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    Are those seperate calculations for those two?

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  118. OpenSessame Group Title
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    The top doesnt matter just look at the lines

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  119. e.mccormick Group Title
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    Yah, well, then that is some sort of what? Rotation, reflection etc?

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  120. OpenSessame Group Title
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    Reflection?

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  121. e.mccormick Group Title
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    Remember that A is going to X and B is going to Y..... should be a huge clue.... YES! Some sort of reflection.

    • one year ago
  122. e.mccormick Group Title
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    So, you just need to find the line they are reflected over.

    • one year ago
  123. e.mccormick Group Title
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    It would be half way between them.

    • one year ago
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    0?

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  125. e.mccormick Group Title
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    Are they both the same distance from x=0?

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  126. OpenSessame Group Title
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    yES...

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  127. e.mccormick Group Title
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    Did you count the distance from 0 to X and 0 to A?

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  128. OpenSessame Group Title
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    no...

    • one year ago
  129. e.mccormick Group Title
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    Take a second look.... they are not the same.

    • one year ago
  130. OpenSessame Group Title
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    Oh...

    • one year ago
  131. e.mccormick Group Title
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    You want the line half way between. So take the distance between the two points and divide by 2. It will be that far to the left of the right most line, and right of the left most line.

    • one year ago
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    okay...

    • one year ago
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is replying to Can someone tell me what button the professor is hitting...

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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

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