### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Mid Point Formula

If is the midpoint of the line joining and then Hence  Convention:

In case of internal division: is the midpoint of .

Hence be a point on , which divides internally.

There are two conditions:

(i) (ii) Note:

(i) We write divides or the line segment joining and in ratio to mean that .

(ii) For divides or the line segment joining and in ratio to mean that .

In Case of External Division: and Alternatively, and Coordinates of any Points on the line:

If and be the coordinates of divides in the ratio (Either internally or externally). Then it can be expressed as or where, For Internal Division:  For External Division (Hence )

Some Example on the above Properties: Distance Formula

Coordinates of and are and respectively, then  Distance from Origin Let be a point on a Cartesian Plane then  Internal Division on Ratio Let and be  the end points of a line segment . divides internally in ratio , the coordinate of is  Internal Division in Ratio Let and be the end points of . divides in ratio internally the coordinate of is  External Division in ratio Let and be two end points on . Let be a point divides externally in ratio , then  External Division in Ratio Let and be the two end points of . Let be a point divides in ratio , externally, then Mid-Point Formula:

Let and be end points of and be midpoint of , then  Scroll to Top