What's a formula to uncover a way to divide a line segment into three equal parts. What would the formula look like?

- anonymous

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- anonymous

@some_someone ?

- anonymous

@satellite73 ?

- anonymous

@Luigi0210 lol sorry to bother you! /.\

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- anonymous

Any clues at all?

- Luigi0210

Nope, sorry :/

- anonymous

oh its fine I can try asking someone else:)

- anonymous

@dan815

- jim_thompson5910

do you mean find the length of each piece? or actually trisect the segment through a geometric construction?

- anonymous

I think to find the length of each piece. The exact questions says: Now that you know how to find the midpoint from two endpoints, tweak your understanding of the formula to uncover a way to divide a line segment in to three equal parts. What would the formula look like?

- jim_thompson5910

One way to do it is to divide the horizontal component of the length by 3
this will give you how far to space the points out in a horizontal sense
you must do the same for the vertical component as well

- jim_thompson5910

so say you had this segment
|dw:1378786046754:dw|

- jim_thompson5910

draw in the horizontal and vertical components
|dw:1378786083004:dw|

- jim_thompson5910

then cut those lengths into 3 congruent pieces
|dw:1378786121773:dw|

- jim_thompson5910

then use these cuts to figure out where the 1/3 and 2/3 markers go on the original line segment
|dw:1378786176000:dw|

- jim_thompson5910

|dw:1378786217033:dw|

- anonymous

yeah, i get what your saying, but there isn't any specific formula where you have to plug in the numbers?

- jim_thompson5910

well this distance here
|dw:1378786360035:dw|
is the difference in the x coordinates

- jim_thompson5910

this distance is the difference in the y coordinates
|dw:1378786383951:dw|

- jim_thompson5910

so you're subtracting the coordinates, then dividing by 3 to get those markers on the horizontal/vertical components
and you're using those markers to get the 1/3 and 2/3 markers

- anonymous

but the question is asking me for a formula?

- jim_thompson5910

I know, I'm trying to get you to think of what that formula would be based on what I'm giving you

- anonymous

Ahhh okay

- anonymous

how about a+b+c=? divide by 3

- jim_thompson5910

not quite

- jim_thompson5910

remember you're taking the differences in the corresponding coordinates, then dividing by 3

- anonymous

oh so then instead of adding them, im subtracting them?

- jim_thompson5910

let
m = |x2 - x1|
this is the horizontal component length
and let
n = |y2 - y1|
this is the vertical component length

- jim_thompson5910

cut these distances into 3rds:
m ---> m/3
n ---> n/3
so if you have the segment with the endpoints (x1,y1) and (x2,y2), then you're adding on m/3 to the coordinates to get these points
1/3 marker: (x1 + 1*m/3, y1 + 1*n/3)
2/3 marker: (x1 + 2*m/3, y1 + 2*n/3)
you could avoid using m and n and just use the distances above, but that notation gets even uglier

- anonymous

yeah, this looks really complicated lol:p

- jim_thompson5910

it's not too bad once you get used to it

- anonymous

thanks for helping me tough. i hope the teacher goes over this tommorow because right now i just want to know out!

- jim_thompson5910

do you see how I defined m and n?

- anonymous

Yeah, yes I did:)

- jim_thompson5910

so if you cut m into 3 then you basically get this distance here
|dw:1378787464289:dw|

- jim_thompson5910

and if you divide n by 3, you get this length here
|dw:1378787503944:dw|

- jim_thompson5910

with me so far?

- anonymous

yes, with you so far:)

- jim_thompson5910

so that's why if you start with (x1,y1)
|dw:1378787643610:dw|

- jim_thompson5910

and you move m/3 units along the x axis and n/3 units along the y axis, then you'll land at the 1/3 marker
|dw:1378787687368:dw|

- jim_thompson5910

that explains why the coordinate of the 1/3 marker is (x1 + m/3, y1 + n/3) and you can write it as (x1 + 1*m/3, y1 + 1*n/3)

- anonymous

thank you so much i appreciate it:)

- jim_thompson5910

you're welcome, the 2/3 mark is found in much the same way, you add on another m/3 to the x coordinate and another n/3 to the y coordinate to get
2/3 marker: (x1 + m/3+m/3, y1 + n/3+n/3)
which turns into
2/3 marker: (x1 + 2*m/3, y1 + 2*n/3)

- dan815

|dw:1378813283291:dw|

- dan815

|dw:1378813443142:dw|

- dan815

jims way is the nicest way though

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