anonymous
  • anonymous
Find the midpoint segment that joins the given points:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
(a, 4) and (a + 2, 0)
anonymous
  • anonymous
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...
anonymous
  • anonymous
are you sure they don't give you the midpoint already and you are to solve for the variables?

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anonymous
  • anonymous
No thats all they give me. I dont understand. Would it be (?, 2)
anonymous
  • anonymous
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.
anonymous
  • anonymous
to find the midpoint given two points, \[(x _{1},y _{1}) and (x _{2},y _{2})\] \[M(\frac{ x _{1} +x _{2}}{ 2 },\frac{ y _{1}+y _{2} }{ 2 })\]
anonymous
  • anonymous
Yeah i know that. But what is the average of a and 2a?
anonymous
  • anonymous
or instead of 2a would it be aa?
anonymous
  • anonymous
lets start of by using the midpoint formula: \[((x1+x2)\div2),((y1+y2)\div2))\]
anonymous
  • anonymous
the average is going to be \[(y2-y1)\div(x2-x1)\]
anonymous
  • anonymous
|dw:1366490592027:dw|
anonymous
  • anonymous
i think you add, not subtraction.
anonymous
  • anonymous
work out the average between THAT point and the SECOND point you posted
anonymous
  • anonymous
|dw:1366490602978:dw| |dw:1366490721666:dw|
anonymous
  • anonymous
AND work out the average of THAT point (Midpoint) AND the FIRST point you posted. then equate the two to solve for a
anonymous
  • anonymous
So the final answer is?
anonymous
  • anonymous
|dw:1366490910101:dw|
anonymous
  • anonymous
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
anonymous
  • anonymous
he still needs to solve for a... Use the average formula between the points / gradient to solve for a.
anonymous
  • anonymous
\[(y2−y1)÷(x2−x1)\]
anonymous
  • anonymous
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?
anonymous
  • anonymous
ok. hang on. let me write this down. gimme 2min.
anonymous
  • anonymous
thank you
jdoe0001
  • jdoe0001
I don't think you need to find what "a" is, as far as I can tell, "a" domain is all real numbers
anonymous
  • anonymous
no, you need to find a. i solved it. i will post it now for you
jdoe0001
  • jdoe0001
ok
anonymous
  • anonymous
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 \[8\div3 (FINAL ANSWER)\]
anonymous
  • anonymous
slight correction. After i said "I made them equal so" it should be (-2 / 3). Forgot to add minus sign to the 2.
anonymous
  • anonymous
so \[\frac{ -2 }{ 3 }\] is the final answer
anonymous
  • anonymous
no, 8/3
anonymous
  • anonymous
ohh i see. Ok thank you!
anonymous
  • anonymous
peace
anonymous
  • anonymous
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.
anonymous
  • anonymous
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).
anonymous
  • anonymous
But i have another question. i need to write this as a coordinate. So should it be (8, 3) ?
anonymous
  • anonymous
|dw:1366492541753:dw|
anonymous
  • anonymous
:)
anonymous
  • anonymous
ok thanks. Makes sense now :)

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