Question

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Answer 1

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?

Answer 2

so -4+6 is 2
2/3?

Answer 3

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?

Answer 4

lol sorry i dont know why i said 3 but yes

Answer 5

ok, now do the same thing with the y-coordinates

the average of 4 and 4 is...?

Answer 6

lol4

Answer 7

right, so the midpoint is (1,4)

can you try #20-22 on your own? :) I'll guide you if you get stuck

Answer 8

k just check me

Answer 9

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

Answer 10

right?

Answer 11

yup

Answer 12

-5+7
2
2/2
1

Answer 13

?

Answer 14

yup, so our midpoint is...?

Answer 15

-5,1

Answer 16

yup, don't forget the parentheses

ready for the next one?

Answer 17

yup

Answer 18

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

Answer 19

yup

Answer 20

so that would be 1.5

Answer 21

-7+5
-2/2
1

Answer 22

right?

Answer 23

lol -1

Answer 24

yup, -1, so put them together

Answer 25

(1.5,-1)

Answer 26

yup, next?

Answer 27

-3-8
-11/2
-5.5

Answer 28

yup

Answer 29

3+6
9/2
4.5

Answer 30

yuppp, ready for 23?

Answer 31

yup that one i dont get what they are asking

Answer 32

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...?

Answer 33

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?

Answer 34

yup

Answer 35

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

Answer 36

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

Answer 37

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)

Answer 38

ah i get it

Answer 39

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

Answer 40

i got it. Can u help with some more

Answer 41

sure

Answer 42

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)

Answer 43

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

Answer 44

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.

Answer 45

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)

Answer 46

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?

Answer 47

yes

Answer 48

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

Answer 49

-3?

Answer 50

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 = ?

Answer 51

10?

Answer 52

yup, so our point becomes S(-3,10)

do you think you can try the others now? just follow the template :)

Answer 53

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

Answer 54

you can go help other people that need help

Answer 55

thank you

Answer 56

:)