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Only one line can pass through two points, but this line can have different equations that could represent it. These are called dependent equations (because they represent the same line).
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That is true for the Euclidean plane. But on surfaces that are not flat, there can be infinitely many lines through any pair of points.
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Do collinear points lay on parallel lines?
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.
Can one line pass through 3 non collinear points?
Not if the line is straight.
Does a secant line pass through the center of a circle?
No, a secant line does not pass through the center of a circle. A secant line is a line that intersects a circle in two distinct points. Only a line passing through the center of a circle is called a diameter.
What is a line segment that connects two points on a circle but does not pass through the center?
A chord
What is a straight line joining points on a circle?
A straight line joining points on a circle is called a "chord" of that circle. If the line happens to pass through the center of the circle, then it's a "diameter" of that circle. The question asked about "points" on a circle, so two points on the circumference of that circle are being considered. (No line can join more than two points of a circle.)
How many lines can pass through two points?
There is exactly one line that can pass through two distinct points. This line is uniquely determined by the two points.
Do collinear points lay on parallel lines?
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.
Can a circle pass through three points of a straight line?
No, a circle can never pass through three points of a straight line. The circle will touch 1) no points of the line, 2) one point of the line (which is now tangent to the circle), or 3) two points of the line. A line can contain (at most) twopoints that lie on the line.
Does a circle pass the vertical line test?
No. Because a vertical line will pass through two points on the graph.
How many lines can pass through a and b?
One line only. This is because by definition a line only needs two points. Three points not in a line would make a plane when connected. Two points, when connected, form a line in which there is only one way to pass through points a and b.
Can one line pass through 3 non collinear points?
Not if the line is straight.
How many planes can pass through two given points?
There are an infinite number of planes that pass through a pair of points. Select any plane that passes through both the points and then rotate it along the line joining the two points.
Does a secant line pass through the center of a circle?
No, a secant line does not pass through the center of a circle. A secant line is a line that intersects a circle in two distinct points. Only a line passing through the center of a circle is called a diameter.
What is a line segment that connects two points on a circle but does not pass through the center?
A chord
A line segment that connects two points on a circle but does not pass through the center?
Chord.
How many lines can be drawn to pass through two points?
There is only one possible line that can can through two different points, presuming there are no overlaps.
What is a straight line joining points on a circle?
A straight line joining points on a circle is called a "chord" of that circle. If the line happens to pass through the center of the circle, then it's a "diameter" of that circle. The question asked about "points" on a circle, so two points on the circumference of that circle are being considered. (No line can join more than two points of a circle.)
