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anonymous

  • 5 years ago

Can someone help me review the distance formula and how to calculate a midpoint?

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  1. anonymous
    • 5 years ago
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    ok, sure...do you have any points to work with?

  2. anonymous
    • 5 years ago
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    Hold on and I'll get a few my teacher gave me to work with

  3. anonymous
    • 5 years ago
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    sure

  4. anonymous
    • 5 years ago
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    W(3, -12) M(2, -1)

  5. anonymous
    • 5 years ago
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    M is the midpoint

  6. anonymous
    • 5 years ago
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    ok, good start. so draw it on a graph first

  7. anonymous
    • 5 years ago
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    Ok one second

  8. anonymous
    • 5 years ago
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    you need to find the other point, let's call it P...

  9. anonymous
    • 5 years ago
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    Ok i have the graph drawn

  10. anonymous
    • 5 years ago
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    nice, so what is the midpoint formula?

  11. anonymous
    • 5 years ago
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    (X1+x2)/2 ; (Y1+y2)/ 2

  12. anonymous
    • 5 years ago
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    ok cool, so you have W:(3, -12), and you have the midpoint...so M=(2,-1)...right so use the formulas. let's look at (x1+x2)/2

  13. anonymous
    • 5 years ago
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    we have that \[2 = (x1 + x2) / 2]\, and that x1 = the x-coordinate from W

  14. anonymous
    • 5 years ago
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    x1 = 3, x2 = ? --> 2 = ( 3 + x2 )/2...solve for x2

  15. anonymous
    • 5 years ago
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    what did you get?

  16. anonymous
    • 5 years ago
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    this would be the x-coordinate for the point P we made up

  17. anonymous
    • 5 years ago
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    I got -2 for X2

  18. anonymous
    • 5 years ago
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    hey, you can refresh the page when it gets stuck ;)

  19. anonymous
    • 5 years ago
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    ok.. I was freaking there for a sec

  20. anonymous
    • 5 years ago
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    the x-coordinate for W is 3, so you say x2 = -2, let's put that back in the Midpoint equation for X: => so we have 3 from W and now we have -2 from x2 , this is (3 + -2) = 1, then 1/2 but the goal is 2

  21. anonymous
    • 5 years ago
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    So this is how I got -2 for an answer 2=(3+X2)/2 -3 -3 (-1)=X2/2 x2 x2 -2= X2

  22. anonymous
    • 5 years ago
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    so you should multiply both sides by 2 1. 2 = ( 3 + x2 ) /2 2. Multiply both sides by 2 (to get ride of the 2 on the right side) 2*2 = ( 3 + x2 ) /2 *2 = 4 = (3 +x2) 3. now we have [ 4 = (3 + x2) ], solve for x2 get x2 = 1

  23. anonymous
    • 5 years ago
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    Oh... okay. I didn't know to do that.

  24. anonymous
    • 5 years ago
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    you skipped ahead and subtracted 3 from both sides, but 3 is in the parantheses. it's like we can get the 3 because the whole thing ( 3 + x2 ) is being divided by 2, so the equation actually is 3/2 + x2/2

  25. anonymous
    • 5 years ago
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    *can't get the 3...

  26. anonymous
    • 5 years ago
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    you want to try the same process to find y?

  27. anonymous
    • 5 years ago
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    Alright.. Thanks for telling me that, my math teacher thought it was okay not to tell us that. And if you want too.

  28. anonymous
    • 5 years ago
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    yes, let's solve for the y-coordinate of P...we have P = ( x2, y2 ) --> P = ( 1, y2 )

  29. anonymous
    • 5 years ago
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    so you can look at your graph, and find 1 on the x-axis...now you're half way there to finding where P actually is

  30. anonymous
    • 5 years ago
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    Okay

  31. anonymous
    • 5 years ago
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    ok, so you're stuck at x=1, now you can only move up or down, changing y, so you have M on the graph and W on the graph, so you can make a guess at where P is just by checking out the graph...

  32. anonymous
    • 5 years ago
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    Is it possible to use the slope intercept to find Y? or would that just add confusion?

  33. anonymous
    • 5 years ago
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    you could, but you have a simple midpoint equation to find y... (y1 + y2) /2 = -1, with y1=-12, so ( -12 + y2 ) /2 = -1...solve it!

  34. anonymous
    • 5 years ago
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    I ended up getting -14

  35. anonymous
    • 5 years ago
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    what are your steps? remember that you have to multiply by 2 here before dealing with -12

  36. anonymous
    • 5 years ago
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    (-12 + Y2)/2=-1 *2 *2 (-12 + y2)= -2 +-12 +-12 Y2= -14

  37. anonymous
    • 5 years ago
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    ah, if you have -12 to both sides, you actually have (-24 + y2) = -14...so you should add 12 to both sides, to get y2 = -2 + 12 = 10

  38. anonymous
    • 5 years ago
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    the goal was to get rid of -12 on the left side, but you can't just get rid of it, you have to keep the relationship that you already have....so if you get rid of -12 on the left side by adding 12 (thus getting 0), you have to do the same thing to the right side or else you've changed the relationship...it's all about find ways to reduce the problem

  39. anonymous
    • 5 years ago
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    right, so what are the coordinates of our point P?

  40. anonymous
    • 5 years ago
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    Okay, so the -2 we divided by is still on the right side of the equal sign?

  41. anonymous
    • 5 years ago
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    right, you multiplied each side by 2 to get rid of the /2 on (y1 + y2), that would make the right side (-1) * (2) = -2

  42. anonymous
    • 5 years ago
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    sorry, :(, I have to go, but I will be back in 15-20minutes

  43. anonymous
    • 5 years ago
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    once you get the midpoint stuff down, you can work on the the distance formula, which is: \[d = \sqrt{ (x2 - x1)^2 + (y2 - y1)^2 }\]

  44. anonymous
    • 5 years ago
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    so, brb

  45. anonymous
    • 5 years ago
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    Okay I'll be here

  46. anonymous
    • 5 years ago
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    all right, are you finished with midpoint stuff?

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