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first we need to find the length of AC
so use the distance formula for this
what numbers do we input though?
the coordinates of A and C
is it 7 or 6 for A?
C is 4 or 4.something?
what is the ordered pair for point A
again I'm asking for point A
No, I'm not.. I'm not sure what point A is at.
you start at the origin (0,0) this is where the x and y axis cross
now how many spaces must you go to the left to get to point A? how many spaces do you go up or down?
Yes.. I understand how to find it but I'm not sure if it's 6 or 7.
it's 6 units to the left so A is the point (-6, 0)
yeah.. I forgot the negative sign. so -6,
the y coordinate is 0 since you don't go up or down and you stay on the x axis
what is point C
don't we have to find AB, BC, and AC?
no all we need right now is AC
why are we doing one point at a time? for the form.?
we need AC because we're trying to prove that some new line segment is parallel to AC and it's half the length so we need the length of AC first
to find the length of AC, we use the distance formula but to do that, we need the points A and C (the x,y form of both points)
okay.. but how do I figure out C? considering it's not an even number
C is the point (0,-4) you start at (0,0) then go down 4 ticks or units to land on C
I honestly don't know what the -6.67 is referring to
so it's -6,-4?
no (0,-4) notice how you don't go left/right from the origin to get to C
no, I mean for AC....
oh AC is the distance from A to C
when I say AC, I really mean "find the length of segment AC"
Now, I'm lost. I just meant the coordinates...
we know that A is the point (-6,0) C is the point (0,-4) the distance from A to C is ????
Should I use a formula or just subtract?
I'd use the formula so you get more practice using it
d = sqrt(-6, 0)^2 + (0 - (-4))^2??
i think you meant to say -6 - 0 instead of -6, 0
if so, then you are correct so far
d = sqrt(x2-x1)^2+(y2-y1)^2 d = sqrt(-6 - 0)^2 + (0 - (-4))^2 d = sqrt(-6)^2 + (4)^2 d = sqrt(36) + (16) d = sqrt(52) d = 7.2
now you must find the midpoints of AB and BC
Do I do AB now?
yes you need the midpoint of AB you do NOT need to find the distance from A to B
how do I do this?
use the midpoint formula http://www.purplemath.com/modules/midpoint.htm the link above explains what the formula is and how it works
Yeah but what numbers do I put in? I actually remember this formula
the coordinates of A and B
that's point B
now use the midpoint formula
-6 + 0/2, 0 + 4/2?
good, that's the midpoint of AB let's call this point M
what is the midpoint of BC?
is it 0,4 and 0,4?
not the midpoint
B(0,4) C(0,-4) midpoint is ????
I must be doing something wrong
the x coordinates of the two points are 0 and 0 add them, divide by 2 (0+0)/2 0/2 0 so the x coordinate of the midpoint is 0
what is the y coordinate of the midpoint ?
I see what I did wrong. It's 0, -2
no it's not
the y coordinates are 4 and -4 they add to 0 cut this in half to get 0
so the midpoint is (0,0)
so let the point N be the midpoint of BC this means N is the point (0,0)
you have two new points: M(-3,2) and N(0,0) you need to do two things now a) find the slope of MN b) find the length of MN
My computer froze and I lost all my answers on the test. I'll come back to this question after.
Hey, could we work from a certain step?
I'm sorry, I cannot help you on tests since it's something you should do on your own.
It's not a test... I was talking about something else. Not what I was consulting with you with.
This is for practice.
How do we find the slope? and the test I was doing was for English
what are the two points?
M(-3,2) and N(0,0)?
use the slope formula to get this m = (y2-y1)/(x2-x1) m = (0-2)/(0-(-3)) m = (0-2)/(0+3) m = -2/3
so that's for one side or both?
I'm not sure what you mean
is this for the same problem? or a different problem?
Same. There was two points so I was wondering.
oh that's right you needed to find the slope of MN
Now I'm confused hahaha
and yes you need two points to find the slope one is not enough
can we start from when we found N?
yeah it doesn't help that this happened nearly 5 hours ago
you saw how to get M and N right?
right, I don't have N written down. Can we do that over? It was 0, 4 right?
and then go from there...
to find N, we need to find the midpoint of BC
I think I'm inputting it wrong.. I got the right answer now I'm getting it wrong
remember the midpoint formula?
so what is the midpoint of BC
I'm getting 0, -2 but isn't it 0,0?
it should be (0,0) yes
4 + (-4) = 0 divide that by 2 to get 0/2 = 0 so that's why the y coordinate of N is 0
oh, I inputted wrong. Could you show the input?
to get the midpoint?
I'm inputting the numbers wrong for the midpoint formula, yes
x coordinate of midpoint: (x1+x2)/2 x coordinate of midpoint: (0+0)/2 x coordinate of midpoint: (0)/2 x coordinate of midpoint: 0 ------------------------------------------------------- y coordinate of midpoint: (x1+x2)/2 y coordinate of midpoint: (4 + (-4))/2 y coordinate of midpoint: (0)/2 y coordinate of midpoint: 0
Therefore the midpoint of BC is N(0,0)
Okay... I got it now.
So now what do we do? Find the slope?
yes but we did that above
I showed the steps for that earlier
yeah.. but it was confusing. Do we just use that formula for both points?
I used the slope formula where are you stuck on those steps?
So the overall answer is -2, 3?
No I got that part.
the slope of MN is -2/3
Alright, I understand. Thanks.
that's great you then use the slope formula to find the slope of AC and compare the two slopes
also you'll need to find the length of MN
So find the slope of AC and then the length of MN? Is there anything else?
not that I can think of you should find that the slope of AC is also -2/3 this will help prove that AC and MN are parallel
also, you should find that MN is half as long as AC so that proves the second part
how do I find the slope for AC? The answer was 7.2
basically you subtract the y coordinates and subtract the x coordinates after all that you divide the two differences (y difference over x difference)
that's how you find the slope
How should I find the length of MN though?
by using the distance formula
find the distance from M to N
by using the distance formula? so after the last step we did, what would I do?
what are the points for A and C
I only have the distance
but you have the coordinates for points A and C
-6,0 and 0, -4?
good, so use the slope formula to get m = (y2-y1)/(x2-x1) m = (-4-0)/(0-(-6)) m = (-4-0)/(0+6) m = (-4)/6 m = -2/3
so you can see that the slope of AC is -2/3 and the slope of MN is also -2/3 This means that AC and MN are parallel
Okay.. yeah then I find the length of?
yes you need the length of MN
I use distance formula for that?
d = sqrt(-3-0)^2+(0-2)^2?
MN: d = sqrt(-3-0)^2+(0-2)^2 d = sqrt(-3)^2 + (-2)^2 d = sqrt(9) + (4) d = sqrt(13) d = 3.6
notice how AC is 7.2 units long (roughly) and MN is roughly 3.6 units long so MN is about half as long as AC (since 7.2/2 = 3.6)
did we satisfy the question? I think I got everything. This practice helped a lot.
yeah there's a lot to it, but I think we got everything
thanks.. I'm sorry this took so long
that's ok, you're welcome