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ineedyouubiebs
What's a formula to uncover a way to divide a line segment into three equal parts. What would the formula look like?
@Luigi0210 lol sorry to bother you! /.\
Any clues at all?
oh its fine I can try asking someone else:)
do you mean find the length of each piece? or actually trisect the segment through a geometric construction?
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?
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
so say you had this segment |dw:1378786046754:dw|
draw in the horizontal and vertical components |dw:1378786083004:dw|
then cut those lengths into 3 congruent pieces |dw:1378786121773:dw|
then use these cuts to figure out where the 1/3 and 2/3 markers go on the original line segment |dw:1378786176000:dw|
|dw:1378786217033:dw|
yeah, i get what your saying, but there isn't any specific formula where you have to plug in the numbers?
well this distance here |dw:1378786360035:dw| is the difference in the x coordinates
this distance is the difference in the y coordinates |dw:1378786383951:dw|
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
but the question is asking me for a formula?
I know, I'm trying to get you to think of what that formula would be based on what I'm giving you
how about a+b+c=? divide by 3
remember you're taking the differences in the corresponding coordinates, then dividing by 3
oh so then instead of adding them, im subtracting them?
let m = |x2 - x1| this is the horizontal component length and let n = |y2 - y1| this is the vertical component length
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
yeah, this looks really complicated lol:p
it's not too bad once you get used to it
thanks for helping me tough. i hope the teacher goes over this tommorow because right now i just want to know out!
do you see how I defined m and n?
Yeah, yes I did:)
so if you cut m into 3 then you basically get this distance here |dw:1378787464289:dw|
and if you divide n by 3, you get this length here |dw:1378787503944:dw|
with me so far?
yes, with you so far:)
so that's why if you start with (x1,y1) |dw:1378787643610:dw|
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|
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)
thank you so much i appreciate it:)
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)
jims way is the nicest way though