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OpenSessame

  • one year ago

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)

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

  2. OpenSessame
    • one year ago
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    Those are the reflections

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

  4. OpenSessame
    • one year ago
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    I think so...

  5. e.mccormick
    • one year ago
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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.

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

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

  8. OpenSessame
    • one year ago
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    Where did the line come from????

  9. OpenSessame
    • one year ago
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    You lost me..

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

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

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

  13. e.mccormick
    • one year ago
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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.

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

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

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

  17. e.mccormick
    • one year ago
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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.

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

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

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

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

  22. e.mccormick
    • one year ago
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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.

  23. OpenSessame
    • one year ago
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    |dw:1376455841757:dw|

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

  25. OpenSessame
    • one year ago
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    |dw:1376455914360:dw|

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

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

  28. OpenSessame
    • one year ago
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    -3?

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

  30. OpenSessame
    • one year ago
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    so 4?

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

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

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

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

  35. e.mccormick
    • one year ago
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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.

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

  37. e.mccormick
    • one year ago
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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|

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

  39. OpenSessame
    • one year ago
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    okay:) i get it!

  40. OpenSessame
    • one year ago
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    |dw:1376456678313:dw|

  41. OpenSessame
    • one year ago
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    |dw:1376456695550:dw|

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

  43. OpenSessame
    • one year ago
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    3?

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

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

  46. OpenSessame
    • one year ago
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    so (4,-9)????

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

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

  49. e.mccormick
    • one year ago
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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!

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

  51. e.mccormick
    • one year ago
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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!

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

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

  54. e.mccormick
    • one year ago
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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!

  55. OpenSessame
    • one year ago
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    Okay, thanks:)

  56. OpenSessame
    • one year ago
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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

  57. e.mccormick
    • one year ago
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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.

  58. OpenSessame
    • one year ago
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    Okay...

  59. e.mccormick
    • one year ago
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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.

  60. OpenSessame
    • one year ago
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    Okay...

  61. e.mccormick
    • one year ago
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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.

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

  63. e.mccormick
    • one year ago
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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.

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

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

  66. OpenSessame
    • one year ago
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    Idk...

  67. e.mccormick
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    Well, lets look at this real quick: |dw:1376458028692:dw| Now you need to double the size.

  68. OpenSessame
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    The dialation is times 2?

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

  70. e.mccormick
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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|

  71. OpenSessame
    • one year ago
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    so its shifted down -6

  72. e.mccormick
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    Well, is that 6? That bottom corner is at -9....

  73. OpenSessame
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    -10?

  74. e.mccormick
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    or -10, actually.... counted wrong.

  75. e.mccormick
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    So it has to go from 2 above to -10 below... so....

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

  77. OpenSessame
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    12

  78. e.mccormick
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    Yep! So 2D, T\(\langle 0,-12\rangle\) is more like it.

  79. OpenSessame
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    that isnt one of my options

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

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

  82. OpenSessame
    • one year ago
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    YUS:) thanks though!

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

  84. e.mccormick
    • one year ago
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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....

  85. OpenSessame
    • one year ago
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    okay!

  86. e.mccormick
    • one year ago
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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?

  87. OpenSessame
    • one year ago
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    240 degrees

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

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

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

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

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

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

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

  95. e.mccormick
    • one year ago
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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.

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

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

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

  99. OpenSessame
    • 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 \[R _{y=x}(PQR)\]

  100. e.mccormick
    • one year ago
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    Is that a reflection over the y axis?

  101. OpenSessame
    • one year ago
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    I believe it is.

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

  103. OpenSessame
    • one year ago
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    You did??

  104. OpenSessame
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    OOOOO

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

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

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

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

  109. OpenSessame
    • one year ago
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    OHHHH!!! MAKES SENSE!

  110. OpenSessame
    • one year ago
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    so (6,-8)

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

  112. OpenSessame
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    YEA! Thanks so much man!

  113. OpenSessame
    • one year ago
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    Write a sequence of rigid motions that maps ab and xy

  114. OpenSessame
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    LAST ONE AND I WILL UNDERSTAND GEOMETRY!

  115. e.mccormick
    • one year ago
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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!

  116. OpenSessame
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    the second part is (AB=XY)

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

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

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

  120. OpenSessame
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    Reflection?

  121. e.mccormick
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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.

  122. e.mccormick
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    So, you just need to find the line they are reflected over.

  123. e.mccormick
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    It would be half way between them.

  124. OpenSessame
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    0?

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

  126. OpenSessame
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    yES...

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

  128. OpenSessame
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    no...

  129. e.mccormick
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    Take a second look.... they are not the same.

  130. OpenSessame
    • one year ago
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    Oh...

  131. e.mccormick
    • one year ago
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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.

  132. OpenSessame
    • one year ago
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    okay...

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