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

Division Formula

(I) Internal Division

If  divides the line segment joining and internally in ratio i.e.

then,

Example:

Let and be two point. divides internally in ratio 2:3 then

(II) External Division

If divides joining and  externally in ratio i.e.

It has two cases:

(a) For i.e.

(b) For i.e.

Example:

Let and be two points. divides externally in ratio then

Midpoint Formula

If be midpoint of joining and then

Example:

Let and be two points in space and be midpoint of , then

Division Formula by ratio

If divides in ratio then coordinates of are given by:

(i) (Internal Division)

(ii) (External Division)

Note:

If and are distinct points then the coordinates of any point on except are given by

Formulas to find Coordinates

If , and  are vertices of triangle , whose sides are of lengths respectively, then

(i) Centroid

(ii) Incentre

(iii) Excentre

(a) (to A)

(b) (to B)

(c) (to C)

If are vertices of triangle and and are coordinates of midpoint of respectively,then coordinate of Centroid of

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