Mathematics
OpenStudy (anonymous):

Determine which point are collinear (1,9),(6,3) and (10,0)

OpenStudy (bahrom7893):

first find a line that connects (1,9) and (6,3)

(10, 0) cant be collinear coz its on x axis

OpenStudy (bahrom7893):

oh yea good point haha

therefor other two are colinear

OpenStudy (anonymous):

I DONT KNOW THE LINE -_-

OpenStudy (anonymous):

Nice

OpenStudy (anonymous):

Aren;t any two points taken together colinear? The third point might not be. But (1,9) and (10,0) are colinear...as are any two you choose.

OpenStudy (anonymous):

idk

OpenStudy (anonymous):

well how do you show your work

OpenStudy (anonymous):

I'm a little confused by the question. Now if it said, "determine is the points are colinear" it would make sense.

OpenStudy (anonymous):

well its determine whether or not they are

OpenStudy (anonymous):

whether or not the three points are colinear? In that case, you would find the slope from point A to point B and the slope from point B to point C and see if they are the same.

OpenStudy (bahrom7893):

okay working on this.. First figure out the line that connects first 2 points (1,9) and (6,3): (y - y1) = M (x-x1) 9-3 = M (1-6) 6 = M (-5) M = - 6/5

OpenStudy (bahrom7893):

y-9 = (-6/5) (x-1) y = -6x/5 + 6/5 + 9 y = -6x/5 + 51/5

OpenStudy (anonymous):

nice

OpenStudy (bahrom7893):

Now plug in point x = 10 and see if the y value is really 0: y = -6 * 10 / 5 + 51 / 5 y = -60/5 + 51/5 y = (51-60)/5 y = -9/5

OpenStudy (bahrom7893):

see if i try point (10,0), it's not on the line, but the point (10, -9/5) is.

OpenStudy (anonymous):

for the second points the slope is (y-y1)=M(x-x1) 0-3=M(10-6) -3=4M M=-3/4 Since the two slopes (bahrom's first slope and this one) aren't the same, they aren't colinear... ANd then you don't even have to come up with an equation for a line.

OpenStudy (bahrom7893):

good point mtbender, sorry I never took this stuff in school haha, so I had to improvise lol

OpenStudy (anonymous):

so which one is collinear

OpenStudy (anonymous):

No problem...I like the completeness of getting the equation and doing the plugging (means you understand the entire scope). But there a certain joy in elegance. :)

OpenStudy (bahrom7893):

1,9 and 6,3 are collinear

OpenStudy (anonymous):

oh ok this is sooooo confusing

OpenStudy (anonymous):

Well...so are (1,9) and (10,0); (6,3) and (10,0) Any two of the points taken together are colinear They are three points of a triangle so there is a line that connects any two.

OpenStudy (anonymous):

The correct answer is that the three points are not colinear.

OpenStudy (anonymous):

ok what about (3,1),(5,5) and (7,9)

OpenStudy (anonymous):

Look at the slopes between points A-B and B-C like we did in the above problem. Set it up as \[y-y_{1}=M(x-x_{1})\] solve for M. You should find the slopes to be the same (M=2) in both cases. Since the slopes are the same, the points are all colinear.