Point and Lines
Point: A point represents a specific location. It has no size, length, width, or depth. In diagrams, it's often represented by a dot.
Lines: A line is a straight one-dimensional figure that extends infinitely in both directions. It is described by two points lying on it.
Infinite lines pass through a point
You might ask, 'How can an infinite number of lines fit here?' You can zoom in, and also, since you know a line extends infinitely, you can place another line between two lines and make it pass through the point
Any two distinct points in a plane can be connected by a unique straight line.
Collinear
A, B, C are collinear.
If three or more points are collinear, it means they all lie on a single line. For any two points, there is always a line that passes through them, so any two points are always collinear. However, the term becomes more meaningful when discussing three or more points. If three points are not collinear, they are often referred to as "non-collinear."
Three non-collinear points define a plane
Which is more stable: a three-legged table or a four-legged table?
Three-Legged Table: A table with three legs is inherently stable on any surface, even if it's uneven. This is because three points define a plane, so a 3-legged table will always sit without wobbling on any surface. This is why tripods (used for cameras, telescopes, etc.) have three legs; they can stand stably on uneven terrains.
Four-Legged Table: On a perfectly flat surface, a 4-legged table can be just as stable as a 3-legged one. However, if the surface is uneven, there's a higher chance that a 4-legged table will wobble because all four legs might not touch the ground evenly. To counteract this, one often has to adjust one of the legs or place something under one leg to make the table stable.
In terms of aesthetics, design, and traditional usage, 4-legged tables are more common, especially for dining tables and desks, as they can offer more surface area and might be perceived as more robust or sturdy. However, in terms of pure stability on uneven surfaces, 3-legged tables have an advantage.
Distance Between a Point Outside the Line and the Line
The shortest distance from a point to a line is the perpendicular drawn from the point to the line. This perpendicular indicates the shortest distance from the point to the line.
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