What are Collinear and Coplanar Points? (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise | Summary and Q&A

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May 25, 2015
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What are Collinear and Coplanar Points? (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise

TL;DR

Points can be classified as co-linear, non co-linear, co-planar, or non co-planar based on the relationships between lines and planes that pass through them.

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Key Insights

  • 💯 Co-linear points have one line passing through them, while non co-linear points do not.
  • 💯 Three non co-linear points always form one plane.
  • 💯 Four or more non co-linear points may or may not form a plane, but if they do, they are called co-planar points.
  • 🫥 Co-planar lines are two or more lines that lie on the same plane.
  • 🫥 Non co-planar lines do not lie on the same plane.
  • 😥 A line and a point will always lie on one plane.
  • 💯 Co-linear points form a line, while non co-linear points form a plane.

Transcript

What are Co-linear and Co-planar points? How many lines can we draw through one point? We can draw one like this, another one like this and many more! Infinite lines can be drawn through one point. What about two points? How many lines can be drawn passing through both these points? Just one! One and only one line can be drawn passing through two g... Read More

Questions & Answers

Q: What are co-linear points?

Co-linear points are three points that are positioned in such a way that a single line can be drawn passing through all three of them. They are considered co-linear because they lie on the same line.

Q: How many lines can be drawn passing through two given points?

Only one line can be drawn passing through two given points. This is because two points uniquely define a line.

Q: Can three points ever be co-linear?

Yes, three points can be co-linear if they are positioned in a way that exactly one line passes through each of them. Otherwise, they are considered non co-linear points.

Q: What is the difference between co-linear and non co-linear points?

The difference lies in the existence of a line passing through the points. Co-linear points have a single line passing through all of them, while non co-linear points do not have such a line.

Q: What does it mean for three points to be co-planar?

Three points are co-planar if exactly one plane passes through all three of them. This means that the three points lie on the same plane.

Q: Do four or more non co-linear points always form a plane?

No, four or more non co-linear points may or may not form a plane. It depends on their positions. If they do form a plane, they are called co-planar points.

Q: What are co-planar lines?

Co-planar lines are two or more lines that lie on the same plane. This means that the lines share the same flat surface.

Q: Can a line and a point lie on one plane?

Yes, a line and a point will always lie on one plane. It doesn't matter how they are positioned or moved, there will always be exactly one plane passing through them.

Summary & Key Takeaways

  • Co-linear points are three points that lie on the same line, while non co-linear points do not have a line passing through all three of them.

  • Three non co-linear points always form one plane, while four or more non co-linear points may or may not form a plane.

  • Co-planar lines are two or more lines that lie on the same plane, while non co-planar lines do not lie on the same plane.

  • A line and a point will always lie on one plane, regardless of their positions.

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