Maths 2 Mark Question

If we have two distinct points, then we can draw infinite number of planes passing through those two points. While if we have three distinct non collinear points, only a single unique plane can be drawn passing through those three points.
Therefore, a minimum of three distinct non collinear points are required to get a unique plane.

If we have a single point A then we can draw infinite number of lines through it, while if we have two points A and B;
Then only one unique line passes through both of them.
When we have one point,

Therefore, a minimum of two distinct are required to determine a unique line.

Two lines l and m in a plane are said to be parallel lines if they do not intersect each other.

Given a single point, then we can draw infinite number of lines through that point.For example: If we have a point A, then there are infinite number of lines passing through it.

Here, lines m, n, o and p all pass through point A.

A line which is not present in the plane can intersect the plane at only one single point.

Given two distinct points, we can draw many planes passing through them. Therefore infinite number of planes can be drawn passing through two distinct points or two points can be common to infinite number of planes.

Given two distinct points, only one unique line can be drawn passing through both of them.
For example, if we have two distinct points A and B, only one line is there which passes through both of them.

If we look at two intersecting plane, we can see that there is only one unique line at which the two planes intersect.

Therefore, two distinct planes can intersect each other at a single unique line as only a single line is common between two intersecting planes.

Three or more points are said to be collinear if there is a line which contains all of them.

Give two points A and B on a line I. the connected part (segment) of the line with end points at A and B is called the line segment AB.

Three or more lines are said to be concurrent if there is a point which lies on all of them.

If A, B, C be the points on a line l, such that A lies between B and C, and we delete the point A from line l, the two parts of l that remain are each called half-line.

A line in which one end point is fixed and the other part can be extended endlessly.

Two lines are intersecting if they have a common point.The common point is called point of intersection.

Given a line and a distinct point not lying on the line, only a single plane can be drawn through both of them as there can be only plane which can accommodate both the line and the point together.
Let us take a line l and a point A, as we can see there can be only plane which pass through both of them.

Two distinct lines can intersect at only point, as there is only one common point betwwen two intersecting lines. For example, if l and m are two intersecting lines then there is only one common point O between them. This is the point of intersecting.

Two distinct planes can intersect at only one unique line, which is common to both of them and one line is made up of infinite points.
Therefore, two distinct planes can intersect at infinite points.

The number of planes that can pass through three distinct points is dependent on the arrangement of the points.

• If the points are collinear, then infinite number of planes may pass through the three distinct points.
• If the points are non collinear, then only one unique plane can pass through the three distinct points.