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annipuppi Group Title

The coordinates for a rhombus are given as (2a,0), (0,2b), (-2a,0), and (0,-2b). Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Be sure to include the formulas

  • one year ago
  • one year ago

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  1. annipuppi Group Title
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    • one year ago
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  2. myininaya Group Title
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    So you want the slopes of the intersecting line segments to be perpendicular, agreed?

    • one year ago
  3. annipuppi Group Title
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    Yeah

    • one year ago
  4. myininaya Group Title
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    and I mean not the slopes to be perpendicular but the line segments to be perpendicular i said that a little wrong errr but anyways the reason slopes came into mind is because we know what about the slopes if the line segments are perpendicular?

    • one year ago
  5. annipuppi Group Title
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    They are the opposite recipricols and I knew what you meant haha

    • one year ago
  6. myininaya Group Title
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    and i guess they were talking about the midpoints

    • one year ago
  7. myininaya Group Title
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    not where the line segments intersect

    • one year ago
  8. myininaya Group Title
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    |dw:1386186685552:dw| pretend that is perfect

    • one year ago
  9. myininaya Group Title
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    they already give you the midpoints

    • one year ago
  10. myininaya Group Title
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    just show the slopes are undefined and 0 with those points given

    • one year ago
  11. myininaya Group Title
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    like look at one line segment at a time Take the line segment with (-a,b) and (-a,-b)

    • one year ago
  12. myininaya Group Title
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    find the slope

    • one year ago
  13. myininaya Group Title
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    then do the same with the line segment going through (-a,b) and (a,b)

    • one year ago
  14. annipuppi Group Title
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    how do you find the slope of that though?

    • one year ago
  15. myininaya Group Title
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    do you know the slope formula? Also what do you know about the slopes of vertical lines and horizontal lines without using the slope formula?

    • one year ago
  16. annipuppi Group Title
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    yeah and the slope of horizontal lines is 0 and the slope of vertical lines is undefined but how do we know they are horizontal and vertical lines?

    • one year ago
  17. myininaya Group Title
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    all the points on x=a have what in common?

    • one year ago
  18. myininaya Group Title
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    look at the line segment going through the midpoints

    • one year ago
  19. annipuppi Group Title
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    oh I see now. nevermind that was a stupid question. Okay so now that I know the slopes of each line how do I prove its a rhombus?

    • one year ago
  20. myininaya Group Title
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    you were trying to show that one thing is a rectangle

    • one year ago
  21. annipuppi Group Title
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    oops I meant to say how do I prove its a rectangle

    • one year ago
  22. myininaya Group Title
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    we did that by showing the angles were 90 degrees.

    • one year ago
  23. myininaya Group Title
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    We show that by showing the line segments were perpendicular.

    • one year ago
  24. myininaya Group Title
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    we knew the line segments were perpendicular because one was horizontal and the other was vertical

    • one year ago
  25. myininaya Group Title
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    we knew we had a horizontal line segment because all the y values of the coordinates that lied on that line segment were the same

    • one year ago
  26. annipuppi Group Title
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    Okay so there arent any formulas that I have to include or anything?

    • one year ago
  27. myininaya Group Title
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    we knew we had a vertical line segment because all the x values of the coordinates that lied on that line segment were the same

    • one year ago
  28. myininaya Group Title
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    If you want you could use that one formula I mentioned

    • one year ago
  29. annipuppi Group Title
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    The slope formula right? but I don't really need it

    • one year ago
  30. myininaya Group Title
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    You also might want to use that midpoint formula to show why those points in your picture are midpoints.

    • one year ago
  31. annipuppi Group Title
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    Okay. that makes sense. Thanks for your help!

    • one year ago
  32. myininaya Group Title
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    np

    • one year ago
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