To prove that three points are colinear, pick two points and form the equation of the line they describe, and then see if the third point lies on that line.
Colinear points mean that if you draw a (really long) line between any two of them, the line will pass through the others. Or simply: there can exist a straight line that can pass through all of them. These are colinear points: . .... .. One line can pass through all of them: These ar not colinear points: :. If I try to connect any two of them with a line, the third point will not lie on that line.
If only 7 are colinear, then the question implies the lines need not go through every point. In that case there is an infinity of lines for each point.
They must be coplanar before they can be colinear. They lie on the same line or equivalently, they must all satisfy te same linear equation.
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.
colinear and non-colinear are terms that are used when describing points in space, not the graph of a function. Maybe what you meant is "Is the function linear?" The answer to that question is no.
To prove that three points are colinear, pick two points and form the equation of the line they describe, and then see if the third point lies on that line.
Colinear Points
Colinear points mean that if you draw a (really long) line between any two of them, the line will pass through the others. Or simply: there can exist a straight line that can pass through all of them. These are colinear points: . .... .. One line can pass through all of them: These ar not colinear points: :. If I try to connect any two of them with a line, the third point will not lie on that line.
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If only 7 are colinear, then the question implies the lines need not go through every point. In that case there is an infinity of lines for each point.
They are points on the line,. If the line is a straight line the points are said to be colinear If all the points are on a line with an equation of the form (x - X)² + (y - Y)² = r² then the points are all points on the circumference of a circle with centre (X, Y) and radius r.
They must be coplanar before they can be colinear. They lie on the same line or equivalently, they must all satisfy te same linear equation.
Different points 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.