How do you tell if three sets of coordinates are collinear on a plane?

Question

Is there a way to tell, without graphing the points themselves if 3 sets of coordinates would be collinear? How would you go about doing so? Would you use y=mx+b format?

Thank you!

Answer 1

Use the slope formula.  If the difference of the y's divided by the difference of the x's  is the same for two pairs of points, then they are collinear.

examples:

(2,5) (0,1) (15,31)

First pair: (5-1)/(2-0) = 4/2=2

Second pair: (1-31)/(0-15)=-30/-15=2

Both pairs have the same slope, so the lines are collinear

(You can also use the third pair: (31-5)/(15-2)=26/13=2)

Contra-example:

(-1,1), (-2,2), (-3,0)

First pair: (1-2)/(-1+2)=-1/1=-1

Second pair: (2-0)/(-2+3)=2/1=2

If you connect the dots of the first pair, the line has a slope of -1.  If you connect the dots of the second pair, the line has a slope of 2.  These points can't be collinear.

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Answer 2

Yes..

Find the slope between two points (1st and 2nd) by the formula:

m = (y2 - y1) / (x2 - x1)

Now  find the slope between two other points (2nd and 3rd) by the above formula..

If the slope is same, then the points are collinear

Answer 3

If you have points A,B and C, find the slopes of AB, BC, and AC

if all are the same the points are collinear.

Answer 4

I suppose you could do that. Transform to a new coordinate system than has two axes in the plane and the third (Z) perpendicular to it. First of all the three points should have Z values of 0 and, if so, then you could check slopes between two pairs of the points (say 1 and 2 and 1 and 3) and if they are the same then they are collinear.

Another way would be to pick some known point in the plane and then create vectors from it to each of the three points. The dot product of each of these with the normal to the plane will be 0 if the points lie in the plane. Then form vectors from point 1 to point 2 (using the vectors just created) and then from point 1 to point 3. If collinear these vectors should be multiples of each other.

Note: People seem to have ignored the fact that you are talking about a general plane and not necessarily the x-y plane. A general sort of plane is defined in a three space with an x, a y and a z.

Answer 5

We can do this easily by checking whether the slopes are equal or not.

Take the three sets as x1,y1 and x2,y2 and x3,y3

If (y2-y1)/(x2-x1) = (y3-y1)/(x3-x1) then they are collinear.

You can do this by mind.

Hope this would help!

Answer 6

points a,b and c

find line for y=mx + b between a and c

sub in b and hope it works

Answer 7

if you have studied how to find the area of a triangle of a set of co-ordinates, then u can do that

and if the area comes out to be 0. tht means they are collinear

or u can also find out by applying internal section formula