How do you determine if three points are collinear, Such as (-3,4), (0,2), (-3,0)?

Answer 1

By slope:
(2-4)/(0+3) = -2/3
(0-2)/(-3-0) = 2/3
Therefore, the three points are not collinear.

Answer 2

One way is to calculate the slopes of the points. If they are all collinear, then the slopes calculated between pairs of points will be equal. This may not be a sufficient condition, but it's a necessary condition. For the three points you gave, the slope between the first two is: (y2 - y1)/(x2 - x1) = (2-4)/(0-(-3))=-2/3. The slope between point 2 and point 3 is +2/3, so these three points can't be collinear. As another example, the points (-1,-1), (0,2), and (1,5) all lie on the line defined by y = 3x+2 (so the slope is 3). Calculating the slopes between the three pairs of points gives 3 each time, as expected for this contrived example. So, in summary, to be collinear, the slopes calculated from all the pairs of points have to be equal.

Answer 3

Find the equation of the line (y = mx + b) for the 1st two points (-3,4),(0,2), then plug in the 3rd point to that equation (x : -3) and see if y comes out equalling 0.

If you need help finding the equation for the line with the 1st two points, add additional info to your question.

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Answer 4

airplane. 2 factors confirm a diverse line. 3 non-collinear factors confirm a diverse airplane. So does 2 intersecting strains and a line and a single ingredient. A airplane is a flat floor having length and width yet no thickness.

Answer 5

Mathmatically you do it by slope (described above), but in the moment of "I have a brain cramp" you can always draw a picture and plot the points.

Answer 6

take the ratio k:1(trick)
now you have to prove k=1 in every point!
thus three points are collinear!

Answer 7

use the formula
(x1|y2-y3|+x2|y3-y1|+x3|y2-y1|)=0