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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?
so -4+6 is 2 2/3?
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?
lol sorry i dont know why i said 3 but yes
ok, now do the same thing with the y-coordinates the average of 4 and 4 is...?
right, so the midpoint is (1,4) can you try #20-22 on your own? :) I'll guide you if you get stuck
k just check me
first coordinate is -5? -7-3 -10/2
-5+7 2 2/2 1
yup, so our midpoint is...?
yup, don't forget the parentheses ready for the next one?
is the first one 3/2? -8+11 3 3/2
so that would be 1.5
-7+5 -2/2 1
yup, -1, so put them together
-3-8 -11/2 -5.5
3+6 9/2 4.5
yuppp, ready for 23?
yup that one i dont get what they are asking
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...?
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?
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
so (m/2,n/2) is the formula? I thought that a midpoint is different than a formula...
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)
ah i get it
I'm not sure how detailed of an explanation they want when they say "explain your reasoning"
i got it. Can u help with some more
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)
R(5,1) M(1,4) R(6,-2) M (5,3)
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.
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)
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?
so, if (3+x)/2 = 0, what is x = ?
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 = ?
yup, so our point becomes S(-3,10) do you think you can try the others now? just follow the template :)
yes i am good now thank you that is all for the day
you can go help other people that need help