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annipuppi

  • 2 years ago

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

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

  3. annipuppi
    • 2 years ago
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    Yeah

  4. myininaya
    • 2 years ago
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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?

  5. annipuppi
    • 2 years ago
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    They are the opposite recipricols and I knew what you meant haha

  6. myininaya
    • 2 years ago
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    and i guess they were talking about the midpoints

  7. myininaya
    • 2 years ago
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    not where the line segments intersect

  8. myininaya
    • 2 years ago
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    |dw:1386186685552:dw| pretend that is perfect

  9. myininaya
    • 2 years ago
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    they already give you the midpoints

  10. myininaya
    • 2 years ago
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    just show the slopes are undefined and 0 with those points given

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

  12. myininaya
    • 2 years ago
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    find the slope

  13. myininaya
    • 2 years ago
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    then do the same with the line segment going through (-a,b) and (a,b)

  14. annipuppi
    • 2 years ago
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    how do you find the slope of that though?

  15. myininaya
    • 2 years ago
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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?

  16. annipuppi
    • 2 years ago
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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?

  17. myininaya
    • 2 years ago
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    all the points on x=a have what in common?

  18. myininaya
    • 2 years ago
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    look at the line segment going through the midpoints

  19. annipuppi
    • 2 years ago
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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?

  20. myininaya
    • 2 years ago
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    you were trying to show that one thing is a rectangle

  21. annipuppi
    • 2 years ago
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    oops I meant to say how do I prove its a rectangle

  22. myininaya
    • 2 years ago
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    we did that by showing the angles were 90 degrees.

  23. myininaya
    • 2 years ago
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    We show that by showing the line segments were perpendicular.

  24. myininaya
    • 2 years ago
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    we knew the line segments were perpendicular because one was horizontal and the other was vertical

  25. myininaya
    • 2 years ago
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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

  26. annipuppi
    • 2 years ago
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    Okay so there arent any formulas that I have to include or anything?

  27. myininaya
    • 2 years ago
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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

  28. myininaya
    • 2 years ago
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    If you want you could use that one formula I mentioned

  29. annipuppi
    • 2 years ago
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    The slope formula right? but I don't really need it

  30. myininaya
    • 2 years ago
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    You also might want to use that midpoint formula to show why those points in your picture are midpoints.

  31. annipuppi
    • 2 years ago
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    Okay. that makes sense. Thanks for your help!

  32. myininaya
    • 2 years ago
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    np

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