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Take any two points and form the equation for a straight line. If all the remaining points satisfy the equation, then they lie on astraight line. Else, they don't.
Here's an example. Consider n points as P1(x1, y1), P2(x2, y2), ...., Pn(xn, yn). In order to determine if P1, P2, ..., Pn lie on a straight line, form the straight line equation with P1 and P2 as: y-y1= m * (x - x1), where the slope m = (y2-y1)/(x2-x1). Then try to satisfy this equation by the remaining points P3, P4, ..., Pn. That is, verify the following:
Is y3-y1= m * (x3 - x1)?
Is y4-y1= m * (x4 - x1)?
...
Is yn-y1= m * (xn - x1)?
If all of the above is true, then the points lie on a straight line.
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If the points are on the same line then the points are collinear?
Three or more points that lie on the same straight line are called Collinear.
A set of points all of which lie on the same straight line?
Collinear set of points
Noncollinear points lie on the same line?
You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.
What is a set of points that lie in a straight path extending forever in opposite directions?
A straight line of infinite length!
Do four points lie on the same plane?
Yes, when they are the coordinates of a straight line equation.
