Attachment below: geometry

- anonymous

Attachment below: geometry

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- anonymous

##### 1 Attachment

- anonymous

@jim_thompson5910

- jim_thompson5910

first we need to find the length of AC

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## More answers

- jim_thompson5910

so use the distance formula for this

- anonymous

what numbers do we input though?

- jim_thompson5910

the coordinates of A and C

- anonymous

is it 7 or 6 for A?

- anonymous

C is 4 or 4.something?

- jim_thompson5910

what is the ordered pair for point A

- anonymous

6, 4?

- jim_thompson5910

you sure?

- jim_thompson5910

again I'm asking for point A

- anonymous

No, I'm not.. I'm not sure what point A is at.

- jim_thompson5910

you start at the origin (0,0)
this is where the x and y axis cross

- jim_thompson5910

now how many spaces must you go to the left to get to point A?
how many spaces do you go up or down?

- anonymous

Yes.. I understand how to find it but I'm not sure if it's 6 or 7.

- anonymous

-7

- jim_thompson5910

it's 6 units to the left
so A is the point (-6, 0)

- anonymous

yeah.. I forgot the negative sign. so -6,

- jim_thompson5910

the y coordinate is 0 since you don't go up or down and you stay on the x axis

- jim_thompson5910

what is point C

- anonymous

don't we have to find AB, BC, and AC?

- jim_thompson5910

no all we need right now is AC

- anonymous

why are we doing one point at a time? for the form.?

- anonymous

ohhh

- jim_thompson5910

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

- jim_thompson5910

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)

- anonymous

okay.. but how do I figure out C? considering it's not an even number

- jim_thompson5910

C is the point (0,-4)
you start at (0,0) then go down 4 ticks or units to land on C

- jim_thompson5910

I honestly don't know what the -6.67 is referring to

- anonymous

so it's -6,-4?

- jim_thompson5910

no (0,-4)
notice how you don't go left/right from the origin to get to C

- anonymous

no, I mean for AC....

- jim_thompson5910

oh AC is the distance from A to C

- jim_thompson5910

when I say AC, I really mean "find the length of segment AC"

- anonymous

Now, I'm lost. I just meant the coordinates...

- jim_thompson5910

we know that A is the point (-6,0)
C is the point (0,-4)
the distance from A to C is ????

- anonymous

Should I use a formula or just subtract?

- jim_thompson5910

I'd use the formula so you get more practice using it

- anonymous

one sec

- jim_thompson5910

ok

- anonymous

d = sqrt(-6, 0)^2 + (0 - (-4))^2??

- jim_thompson5910

i think you meant to say -6 - 0 instead of -6, 0

- jim_thompson5910

if so, then you are correct so far

- anonymous

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

- jim_thompson5910

good

- jim_thompson5910

now you must find the midpoints of AB and BC

- anonymous

Do I do AB now?

- jim_thompson5910

yes you need the midpoint of AB
you do NOT need to find the distance from A to B

- anonymous

how do I do this?

- jim_thompson5910

use the midpoint formula
http://www.purplemath.com/modules/midpoint.htm
the link above explains what the formula is and how it works

- anonymous

Yeah but what numbers do I put in? I actually remember this formula

- jim_thompson5910

the coordinates of A and B

- anonymous

0,4 ?

- jim_thompson5910

that's point B

- jim_thompson5910

A(-6,0)
B(0,4)

- jim_thompson5910

now use the midpoint formula

- anonymous

-6 + 0/2, 0 + 4/2?

- jim_thompson5910

keep going

- anonymous

-3, 2

- jim_thompson5910

good, that's the midpoint of AB
let's call this point M

- jim_thompson5910

what is the midpoint of BC?

- anonymous

is it 0,4 and 0,4?

- anonymous

not the midpoint

- jim_thompson5910

B(0,4)
C(0,-4)
midpoint is ????

- anonymous

2, -2?

- jim_thompson5910

no

- anonymous

I must be doing something wrong

- jim_thompson5910

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

- jim_thompson5910

what is the y coordinate of the midpoint ?

- anonymous

I see what I did wrong. It's 0, -2

- jim_thompson5910

no it's not

- jim_thompson5910

the y coordinates are 4 and -4
they add to 0
cut this in half to get 0

- jim_thompson5910

so the midpoint is (0,0)

- jim_thompson5910

so let the point N be the midpoint of BC
this means N is the point (0,0)

- jim_thompson5910

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

- anonymous

one sec

- jim_thompson5910

ok

- anonymous

My computer froze and I lost all my answers on the test. I'll come back to this question after.

- anonymous

Hey, could we work from a certain step?

- jim_thompson5910

I'm sorry, I cannot help you on tests since it's something you should do on your own.

- anonymous

It's not a test... I was talking about something else. Not what I was consulting with you with.

- anonymous

This is for practice.

- jim_thompson5910

alright

- anonymous

How do we find the slope? and the test I was doing was for English

- jim_thompson5910

what are the two points?

- anonymous

M(-3,2) and N(0,0)?

- jim_thompson5910

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

- anonymous

so that's for one side or both?

- jim_thompson5910

I'm not sure what you mean

- jim_thompson5910

is this for the same problem? or a different problem?

- anonymous

Same. There was two points so I was wondering.

- jim_thompson5910

oh that's right you needed to find the slope of MN

- anonymous

Now I'm confused hahaha

- jim_thompson5910

and yes you need two points to find the slope
one is not enough

- anonymous

can we start from when we found N?

- jim_thompson5910

yeah it doesn't help that this happened nearly 5 hours ago

- jim_thompson5910

you saw how to get M and N right?

- anonymous

right, I don't have N written down. Can we do that over? It was 0, 4 right?

- anonymous

and then go from there...

- jim_thompson5910

to find N, we need to find the midpoint of BC

- jim_thompson5910

B(0,4)
C(0,-4)

- anonymous

I think I'm inputting it wrong.. I got the right answer now I'm getting it wrong

- jim_thompson5910

remember the midpoint formula?

- anonymous

Yep

- jim_thompson5910

so what is the midpoint of BC

- anonymous

I'm getting 0, -2 but isn't it 0,0?

- jim_thompson5910

it should be (0,0) yes

- jim_thompson5910

4 + (-4) = 0
divide that by 2 to get 0/2 = 0
so that's why the y coordinate of N is 0

- anonymous

oh, I inputted wrong. Could you show the input?

- jim_thompson5910

to get the midpoint?

- anonymous

I'm inputting the numbers wrong for the midpoint formula, yes

- jim_thompson5910

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

- jim_thompson5910

Therefore the midpoint of BC is N(0,0)

- anonymous

Okay... I got it now.

- jim_thompson5910

ok great

- anonymous

So now what do we do? Find the slope?

- jim_thompson5910

yes but we did that above

- jim_thompson5910

I showed the steps for that earlier

- anonymous

yeah.. but it was confusing. Do we just use that formula for both points?

- jim_thompson5910

I used the slope formula
where are you stuck on those steps?

- anonymous

So the overall answer is -2, 3?

- anonymous

No I got that part.

- jim_thompson5910

the slope of MN is -2/3

- anonymous

Alright, I understand. Thanks.

- jim_thompson5910

that's great
you then use the slope formula to find the slope of AC and compare the two slopes

- jim_thompson5910

also you'll need to find the length of MN

- anonymous

So find the slope of AC and then the length of MN? Is there anything else?

- jim_thompson5910

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

- jim_thompson5910

also, you should find that MN is half as long as AC
so that proves the second part

- anonymous

how do I find the slope for AC? The answer was 7.2

- jim_thompson5910

basically you subtract the y coordinates and subtract the x coordinates
after all that you divide the two differences (y difference over x difference)

- jim_thompson5910

that's how you find the slope

- anonymous

How should I find the length of MN though?

- jim_thompson5910

by using the distance formula

- jim_thompson5910

find the distance from M to N

- anonymous

by using the distance formula? so after the last step we did, what would I do?

- anonymous

slope AC?

- jim_thompson5910

what are the points for A and C

- anonymous

I only have the distance

- jim_thompson5910

but you have the coordinates for points A and C

- anonymous

-6,0 and 0, -4?

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

Okay.. yeah then I find the length of?

- jim_thompson5910

yes you need the length of MN

- anonymous

I use distance formula for that?

- jim_thompson5910

yes

- anonymous

d = sqrt(-3-0)^2+(0-2)^2?

- jim_thompson5910

keep going

- anonymous

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

- jim_thompson5910

good

- jim_thompson5910

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)

- anonymous

did we satisfy the question? I think I got everything. This practice helped a lot.

- jim_thompson5910

yeah there's a lot to it, but I think we got everything

- anonymous

thanks.. I'm sorry this took so long

- jim_thompson5910

that's ok, you're welcome

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