Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
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

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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

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