Question

PLEASE HELP MEEE AGAIN :(
find all values of t such that the points A(t-1, 2t-1), B(4, 1-2t) and C(-3, 3t+5) are collinear.

Answer 1

hint:

the law of line is:

AB + BC = AC

Answer 2

does that help?

Answer 3

that's what i'm doing now but then it's getting really complicated and i believe there's an easier way?

Answer 4

@sauravshakya same slope could mean parallel lines so it doesnt determine if points are collinear

Answer 5

slope how? but they could still be different lines if they have the same slope?

Answer 6

there's no other way...it will just get harder each day

Answer 7

anyway...no easier way...

Answer 8

okay so i got the distances:
AB sqrt (17t^2-26t+29)
BC sqrt (25t^2+40t+65)
AC sqrt (2t^2+16t+40)

right ab+bc=ac? is it the same if ac+bc=ab? or ab+ac=bc?

Answer 9

@lgbasallote ?

Answer 10

@dydlf donnt change the original question. your making my previous comments look foolish >:(

Answer 11

sorry, what original question? O: i'm still talking about the same one?

Answer 12

oh

Answer 13

AB + BC = AC

Answer 14

AC + BC is different

Answer 15

so is AB + AC

Answer 16

so one can't say ac+bc is equal to ab?

Answer 17

yep

Answer 18

i'm guessing ac is supposed to be the "longest" side of the triangle then? so how would i know which is the longest side if the distances are...

AB sqrt (17t^2-26t+29)
BC sqrt (25t^2+40t+65)
AC sqrt (2t^2+16t+40)

Answer 19

triangle? we're talking about lines o.O

Answer 20

maybe it can help if you visualize it like this



that's why if it's a line AB + BC = AC

Answer 21

sorry sorry whoops. but i'm basing this off the triangle inequality that says distances ac≥ab+bc

and if ac=ab+bc then the points a, b and c are collinear

Answer 22

okay wait let me rephrase... i'm guessing ac is supposed to be the points farthest apart? so how would i know which points are those if the distances are...
AB sqrt (17t^2-26t+29)
BC sqrt (25t^2+40t+65)
AC sqrt (2t^2+16t+40)

since i can't plot them? can i assume b and c are the furthest apart since it's 25^2??

Answer 23

you solve AB + BC

Answer 24

how did you know that it's point B in the middle of A and C then?
i tried ab+bc=ac then it's not getting anywhere... http://www.wolframalpha.com/input/?i=%2817t%5E2-26t%2B29%29+%2B+%2825t%5E2%2B40t%2B65%29+%3D+%282t%5E2%2B16t%2B40%29+

Answer 25

i dont know if B is the "middle" of A and C. but i do know that B is in between A and C

Answer 26

because they are collinear

Answer 27

one of them is bound to be in between

Answer 28

if you want you can also do

AC + CB = AB

or

CB + BA = CA

or something like that