Find the midpoint segment that joins the given points:

- anonymous

Find the midpoint segment that joins the given points:

- schrodinger

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- anonymous

(a, 4) and (a + 2, 0)

- 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

are you sure they don't give you the midpoint already and you are to solve for the variables?

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## More answers

- anonymous

No thats all they give me. I dont understand. Would it be (?, 2)

- 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

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

Yeah i know that. But what is the average of a and 2a?

- anonymous

or instead of 2a would it be aa?

- anonymous

lets start of by using the midpoint formula: \[((x1+x2)\div2),((y1+y2)\div2))\]

- anonymous

the average is going to be \[(y2-y1)\div(x2-x1)\]

- anonymous

|dw:1366490592027:dw|

- anonymous

i think you add, not subtraction.

- anonymous

work out the average between THAT point and the SECOND point you posted

- anonymous

|dw:1366490602978:dw|
|dw:1366490721666:dw|

- 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

So the final answer is?

- anonymous

|dw:1366490910101:dw|

- 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

he still needs to solve for a... Use the average formula between the points / gradient to solve for a.

- anonymous

\[(y2−y1)÷(x2−x1)\]

- 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

ok. hang on. let me write this down. gimme 2min.

- anonymous

thank you

- 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

no, you need to find a. i solved it. i will post it now for you

- jdoe0001

ok

- 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

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

- anonymous

so \[\frac{ -2 }{ 3 }\] is the final answer

- anonymous

no, 8/3

- anonymous

ohh i see. Ok thank you!

- anonymous

peace

- 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

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

But i have another question. i need to write this as a coordinate. So should it be (8, 3) ?

- anonymous

|dw:1366492541753:dw|

- anonymous

:)

- anonymous

ok thanks. Makes sense now :)

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