collinear

[DiGiTaIErRoR]

Are the points A(-2,-3), B(1,-1), and C(8,3) collinear?

I said no, but the teacher said I'm wrong.

[NotLKH]

My Math termonology is a little rusty, but if collinear does mean if they all lay on a single line, then

Since the slope from {1,-1} to {-2,-3} = (-3 - -1)/(-2-1) = -2/-3 = 2/3,
and the slope from {8,3} to {1,-1} = (-1 - 3)/(1 - 8) = -4/-7 = 4/7,

And since no one can validly prove 2/3 = 4/7,
then I don't believe they are collinear.

So, why does your teacher believe they are?

[jim mcnamara]

Three points are collinear if for each point xi for (X, Y, Z)
(where i is 1,2,3) the following is true:

 X2-X1 : Y2-Y1 : Z2-Z1 = X3-X1 : Y3-Y1 : Z3-Z1
 
 Since we can assume Z is always zero (two dimensions) we get:
 
 -1 -(-2):-1 -(-3):0-0 must equal 8-(-2): 3-(-3):0-0
 which is:
    1:2:0 = 10:0:0

These are NOT equal ratios, the lines are therefore not collinear.

[DiGiTaIErRoR]

Well, I'm in alternative education, because regular school is quite boring, and I'm doing advanced alegrebra with trig. The program says I'm wrong, but I know I'm right. I showed the teacher, and she agreed.

This happens quite often, and the problem doesn't get addressed probably because I'm the second one since the founding of the program to actually do the course.

Oh well. She passed me out of it.

[bugzpodder]

hey digital error. try this:

using long division, divide 2.0000... by 2. except at first, instead of writing a "1", use a "0" as shown below:

             0.
            ------------------
         2 /2.0000000000000...

[Kalkewl8ter]

Bugz,

Nice...so it's 0.99999...?