Question

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

Answer 1

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

Answer 2

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

Answer 3

oh yea good point haha

Answer 4

therefor other two are colinear

Answer 5

I DONT KNOW THE LINE -_-

Answer 6

Nice

Answer 7

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.

Answer 8

idk

Answer 9

well how do you show your work

Answer 10

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

Answer 11

well its determine whether or not they are

Answer 12

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.

Answer 13

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

Answer 14

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

Answer 15

nice

Answer 16

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

Answer 17

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

Answer 18

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.

Answer 19

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

Answer 20

so which one is collinear

Answer 21

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. :)

Answer 22

1,9 and 6,3 are collinear

Answer 23

oh ok this is sooooo confusing

Answer 24

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.

Answer 25

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

Answer 26

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

Answer 27

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.