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Mrfootballman97

Find the midpoint segment that joins the given points:

  • one year ago
  • one year ago

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  1. Mrfootballman97
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    (a, 4) and (a + 2, 0)

    • one year ago
  2. Mrfootballman97
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    I dont know how to do it. I would know if it had only numbers but since those variables are there i dont know what to do...

    • one year ago
  3. adziz
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    are you sure they don't give you the midpoint already and you are to solve for the variables?

    • one year ago
  4. Mrfootballman97
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    No thats all they give me. I dont understand. Would it be (?, 2)

    • one year ago
  5. Mrfootballman97
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    You have to find the average of x1 and x2, and then the same for y1 and y2. Then you add the averages for each coordinate. I probably said that wrong but i know how to do it if there is only numbers.

    • one year ago
  6. kausarsalley
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    to find the midpoint given two points, \[(x _{1},y _{1}) and (x _{2},y _{2})\] \[M(\frac{ x _{1} +x _{2}}{ 2 },\frac{ y _{1}+y _{2} }{ 2 })\]

    • one year ago
  7. Mrfootballman97
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    Yeah i know that. But what is the average of a and 2a?

    • one year ago
  8. Mrfootballman97
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    or instead of 2a would it be aa?

    • one year ago
  9. adziz
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    lets start of by using the midpoint formula: \[((x1+x2)\div2),((y1+y2)\div2))\]

    • one year ago
  10. adziz
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    the average is going to be \[(y2-y1)\div(x2-x1)\]

    • one year ago
  11. Mrfootballman97
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    |dw:1366490592027:dw|

    • one year ago
  12. Mrfootballman97
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    i think you add, not subtraction.

    • one year ago
  13. adziz
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    work out the average between THAT point and the SECOND point you posted

    • one year ago
  14. kausarsalley
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    |dw:1366490602978:dw| |dw:1366490721666:dw|

    • one year ago
  15. adziz
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    AND work out the average of THAT point (Midpoint) AND the FIRST point you posted. then equate the two to solve for a

    • one year ago
  16. Mrfootballman97
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    So the final answer is?

    • one year ago
  17. kausarsalley
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    |dw:1366490910101:dw|

    • one year ago
  18. adziz
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    work out the average between the point m. Which is (a+1,2) and the two points in the original question. So you have two averages. Then put them equal to one another (as the gradient should be the same for either, IE rate of change would be equal) then solve for a

    • one year ago
  19. adziz
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    he still needs to solve for a... Use the average formula between the points / gradient to solve for a.

    • one year ago
  20. adziz
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    \[(y2−y1)÷(x2−x1)\]

    • one year ago
  21. Mrfootballman97
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    Well im confused so adziz it seems you know the answer. Would you please tell it to me so i can understand how to do the next problem that is like this one?

    • one year ago
  22. adziz
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    ok. hang on. let me write this down. gimme 2min.

    • one year ago
  23. Mrfootballman97
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    thank you

    • one year ago
  24. jdoe0001
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    I don't think you need to find what "a" is, as far as I can tell, "a" domain is all real numbers

    • one year ago
  25. adziz
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    no, you need to find a. i solved it. i will post it now for you

    • one year ago
  26. jdoe0001
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    ok

    • one year ago
  27. adziz
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    using the midpoint formula and solving that our MIDPOINT(a+1, 2). Using the GRADIENT formula (average formula): \[(y2−y1)÷(x2−x1)\] we make work out the gradient using the formula above, between the MIDPOINT and the first point (a,4). I got this to be \[2-a\]. Then we solved for the gradient between the second point and the midpoint. I got this to be \[(-2\div3)\] I made them equal so \[(2-a) = (2\div3)\]. I then simply solved for a to be \[8\div3 (FINAL ANSWER)\]

    • one year ago
  28. adziz
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    slight correction. After i said "I made them equal so" it should be (-2 / 3). Forgot to add minus sign to the 2.

    • one year ago
  29. Mrfootballman97
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    so \[\frac{ -2 }{ 3 }\] is the final answer

    • one year ago
  30. adziz
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    no, 8/3

    • one year ago
  31. Mrfootballman97
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    ohh i see. Ok thank you!

    • one year ago
  32. adziz
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    peace

    • one year ago
  33. adziz
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    if you still on this page do the following. My answer is 100 % right: Plug 8/3 into a for the point M(a+1,2) you get --> M(11/3 , 2). Now plug 8/3 into the MIDPOINT FORMULA. You should get the exact same coordinate as above. Hence my answer is correct.

    • one year ago
  34. adziz
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    midpoint formula: (8/3) + (8/3 + 2)div2 , 4+0div2 will be (11/3,2). The SAME answer you got when you simply plugged it into the midpoint itself (The point you got when you used the midpoint formula without knowing a).

    • one year ago
  35. Mrfootballman97
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    But i have another question. i need to write this as a coordinate. So should it be (8, 3) ?

    • one year ago
  36. adziz
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    |dw:1366492541753:dw|

    • one year ago
  37. adziz
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    :)

    • one year ago
  38. Mrfootballman97
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    ok thanks. Makes sense now :)

    • one year ago
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