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- anonymous

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- Vocaloid

to find the midpoint, you take the average value of the x-coordinates, then the average value of the y-coordinates, then put them together to make a new point (x-average,y-average)
we can use #19 as an example
G(-4,4) and H(6,4)
the x-coordinates are -4 and 6, do you remember how to find the average?

- anonymous

so -4+6 is 2
2/3?

- Vocaloid

almost but not quite
-4+6 = 2, correct, but we divide by 2, not 3, since there are 2 points
2/2 = 1, with me so far?

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## More answers

- anonymous

lol sorry i dont know why i said 3 but yes

- Vocaloid

ok, now do the same thing with the y-coordinates
the average of 4 and 4 is...?

- anonymous

lol4

- Vocaloid

right, so the midpoint is (1,4)
can you try #20-22 on your own? :) I'll guide you if you get stuck

- anonymous

k just check me

- anonymous

first coordinate is -5?
-7-3
-10/2

- anonymous

right?

- Vocaloid

yup

- anonymous

-5+7
2
2/2
1

- anonymous

?

- Vocaloid

yup, so our midpoint is...?

- anonymous

-5,1

- Vocaloid

yup, don't forget the parentheses
ready for the next one?

- anonymous

yup

- anonymous

is the first one 3/2?
-8+11
3
3/2

- Vocaloid

yup

- anonymous

so that would be 1.5

- anonymous

-7+5
-2/2
1

- anonymous

right?

- anonymous

lol -1

- Vocaloid

yup, -1, so put them together

- anonymous

(1.5,-1)

- Vocaloid

yup, next?

- anonymous

-3-8
-11/2
-5.5

- Vocaloid

yup

- anonymous

3+6
9/2
4.5

- Vocaloid

yuppp, ready for 23?

- anonymous

yup that one i dont get what they are asking

- Vocaloid

well, we're basically doing the same thing that we've been doing so far, except with letters (variables) instead of numbers
so, if our first point is (0,0) and our second point is (m,n), we follow the same procedure
we add the x-coordinates together and divide by 2, getting...?

- Vocaloid

not quite...
the x-coordinates are 0 and m, correct? so when we take the average we get
(0+m)/2 = m/2, with me so far?

- anonymous

yup

- Vocaloid

using the same reasoning for the y-coordinates we get
n/2
giving us a final point (m/2,n/2) which is the formula they're looking for

- anonymous

so (m/2,n/2) is the formula? I thought that a midpoint is different than a formula...

- Vocaloid

well, it's both a midpoint AND a formula, really. a formula is just a set of instructions to find some value, by manipulating known variables
what makes it a "formula" is the fact that we can plug in any m and n to get our midpoint
so our formula is midpoint = (m/2,n/2)

- anonymous

ah i get it

- Vocaloid

I'm not sure how detailed of an explanation they want when they say "explain your reasoning"

- anonymous

i got it. Can u help with some more

- Vocaloid

sure

- anonymous

i think this is the same kind of problem but i would like help.
Use the given endpoint R and the midpoint M of RS to find the coordinates of the other endpoint S
R(3,0), M(0,5)

- anonymous

R(5,1) M(1,4)
R(6,-2) M (5,3)

- Vocaloid

well, the same rule applies, but we have to think a bit differently because we are now given a midpoint + an endpoint, rather than two endpoints.

- Vocaloid

before, we took the average of the 2 endpoints and got a midpoint, but here we kind of need to work backwards. I'll demonstrate using R(3,0) and M(0,5)

- Vocaloid

R = endpoint 1 = (3,0)
M = midpoint = (0,5)
S = endpoint 2 = (x,y)
using our rules from before, we know that (3+x)/2 = 0, with me so far?

- anonymous

yes

- Vocaloid

so, if (3+x)/2 = 0, what is x = ?

- anonymous

-3?

- Vocaloid

yup, now let's do y
R = endpoint 1 = (3,0)
M = midpoint = (0,5)
S = endpoint 2 = (x,y)
(0+y)/2 = 5, so y = ?

- anonymous

10?

- Vocaloid

yup, so our point becomes S(-3,10)
do you think you can try the others now? just follow the template :)

- anonymous

yes i am good now thank you that is all for the day

- anonymous

you can go help other people that need help

- anonymous

thank you

- anonymous

:)

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