how can you prove that 4 points on a line are collinear?
I need 3 methods
2007-12-16 04:42:36 · 2 answers · asked by xoxox 2 in Science & Mathematics ➔ Mathematics
Take the 1st and last points and detremine the equation of the line that passes through both of them. Then take the cordinates of eac of the other two points and see if they satiisfy the equation of that line.. If they both do, then the four points are collinear because yhey all lie on the same straight line.
Method 2 could be to take 1st and second point to determine equation and see if points 3 and 4 satisfy the equation.
Method 3 could be to take the 2nd and 3rd point to determine the straight line and see if the 1st and last point also lie on the line.
You could also find slope of line passing through point 1 and point 2. Then see if it is same as slope of line passing through point 1 and 3 and through point 1 and 4. If so they are all collinear.
You could also check to see if the lines passing through any two of the points all have same slope and same y -intercept.
2007-12-16 04:52:19 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
Another methods could be as under:
Suppose the four points are A, B, C and D.
If the points A, B and C are collinear then area of the Î ABC must be zero, otherwise not.
Similarly, if the points B, C and D are collinear then area of the Î BCD must be zero, otherwise not.
However, if Î ABC = 0 and Î BCD â 0, this shows that D does not lie on the line ABC etc.
2007-12-16 13:21:57 · answer #2 · answered by quidwai 4 · 0⤊ 0⤋