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OpenSessame

  • 2 years 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
    • 2 years ago
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    So the Ry=-5 and Rx=1 are the lines you need to reflect across?

  2. OpenSessame
    • 2 years ago
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    Those are the reflections

  3. e.mccormick
    • 2 years 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
    • 2 years ago
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    I think so...

  5. e.mccormick
    • 2 years 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
    • 2 years ago
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    Okay, but i dont understand what i have to do...

  7. e.mccormick
    • 2 years 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
    • 2 years ago
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    Where did the line come from????

  9. OpenSessame
    • 2 years ago
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    You lost me..

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

  11. e.mccormick
    • 2 years ago
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    Let me show you an example.

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

  13. e.mccormick
    • 2 years 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
    • 2 years ago
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    |dw:1376455572591:dw|

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

  16. OpenSessame
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    |dw:1376455677255:dw|

  19. OpenSessame
    • 2 years ago
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    Do the distance is the number in the equation?

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

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

  22. e.mccormick
    • 2 years 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
    • 2 years ago
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    |dw:1376455841757:dw|

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

  25. OpenSessame
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    |dw:1376455914360:dw|

  26. OpenSessame
    • 2 years ago
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    Now what do i do exactly?

  27. e.mccormick
    • 2 years 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
    • 2 years ago
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    -3?

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

  30. OpenSessame
    • 2 years ago
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    so 4?

  31. e.mccormick
    • 2 years 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
    • 2 years ago
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    so at -5?

  33. OpenSessame
    • 2 years ago
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    wait no....-4?

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

  35. e.mccormick
    • 2 years 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
    • 2 years ago
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    Ohhhh so -9?

  37. e.mccormick
    • 2 years 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
    • 2 years ago
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    Now you have the line Rx=1 to do the second reflection over.

  39. OpenSessame
    • 2 years ago
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    okay:) i get it!

  40. OpenSessame
    • 2 years ago
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    |dw:1376456678313:dw|

  41. OpenSessame
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    |dw:1376456695550:dw|

  42. e.mccormick
    • 2 years ago
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    So, how far this time?

  43. OpenSessame
    • 2 years ago
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    3?

  44. e.mccormick
    • 2 years ago
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    \(\large\ddot\smile\)

  45. OpenSessame
    • 2 years ago
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    so the point would me three to the right?

  46. OpenSessame
    • 2 years ago
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    so (4,-9)????

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

  48. OpenSessame
    • 2 years ago
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    wait im gonna see if it matches...

  49. e.mccormick
    • 2 years 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
    • 2 years ago
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    Okay, the textbook just didnt really explain it

  51. e.mccormick
    • 2 years 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
    • 2 years ago
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    yea, thats the right answer! thanks:)

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

  54. e.mccormick
    • 2 years 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
    • 2 years ago
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    Okay, thanks:)

  56. OpenSessame
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    Okay...

  59. e.mccormick
    • 2 years 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
    • 2 years ago
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    Okay...

  61. e.mccormick
    • 2 years 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
    • 2 years ago
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    wait is the answer D2*T<0,-6>

  63. e.mccormick
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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
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    Really??? woooohoooo

  65. e.mccormick
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    Hmmm.... -6.... is that enough on the translation?

  66. OpenSessame
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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
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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
    • 2 years 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
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    So my bad. Looks like you did have it right.

  82. OpenSessame
    • 2 years ago
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    YUS:) thanks though!

  83. OpenSessame
    • 2 years 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
    • 2 years 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
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    okay!

  86. e.mccormick
    • 2 years 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
    • 2 years ago
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    240 degrees

  88. OpenSessame
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    Thats really all i understand...

  89. e.mccormick
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    r is usually a radius.... but there is no distance....

  90. OpenSessame
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    I think r is the point?

  91. e.mccormick
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    Is it R and not r?

  92. OpenSessame
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    Thats the problem..

  93. e.mccormick
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    hmmm..... Well, 240/30=8 segments.

  94. OpenSessame
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    so 8 to the left or right?

  95. e.mccormick
    • 2 years 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
    • 2 years ago
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    So would it be K???

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

  98. OpenSessame
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    Okay...Well for me thats better then nothing!

  99. OpenSessame
    • 2 years 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
    • 2 years ago
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    Is that a reflection over the y axis?

  101. OpenSessame
    • 2 years ago
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    I believe it is.

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

  103. OpenSessame
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    You did??

  104. OpenSessame
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    OOOOO

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

  106. OpenSessame
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    So just make it the other sign?

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

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

  109. OpenSessame
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    OHHHH!!! MAKES SENSE!

  110. OpenSessame
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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
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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
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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
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    Oh...

  131. e.mccormick
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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
    • 2 years ago
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    okay...

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is replying to Can someone tell me what button the professor is hitting...

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