Straight Lines Class 11th Notes - Free NCERT Class 11 Maths Chapter 10 notes - Download PDF

Straight lines are included in the 10 chapter of NCERT. The NCERT Class 11 Maths chapter 10 notes are based on the straight line. We will study the inclination of line with the x-axis, slope normal form of a straight line, intercepts from of a straight line, distance from a point to a line, the distance between parallel lines. Class 11 Math chapter 10 notes provide all-important derivatives. Class 11 Math chapter 10 notes nicely summarize the important formulas and the derivations of those formulas. A Class 11 Maths chapter 10 note helps a student to have a last-minute revision before an exam.

Notes for Class 11 Maths chapter 10 is made in such a way that a student does not face any difficulty during their preparation. Straight lines Class 11 notes are an important chapter for JEE advance examination.

After going through Class 11 Straight lines of notes

Students can also refer to,

• NCERT Solutions for Class 11 Maths Chapter 10 Straight Line
• NCERT Exemplar Class 11 Maths Chapter 10 Straight Lines

NCERT Class 11 Maths Chapter 10 Notes

1. The distance between two points P(x₁,y₁) and Q(x₂,y₂) is

2. The coordinate of point which cuts a line segment joining by P(x₁,y₁) and Q(x₂,y₂) internally in ratio m:n is

3. If the ratio of m:n = 1:1 then the coordinate of the point is

4. Area of the triangle whose vertices are P(x₁,y₁), Q(x₂,y₂), and R(x₃,y₃)

Slope Of A Line

The steepness of a line is known as the slope of the line.

A line that is nonparallel to the x-axis cuts the x-axis to two angles. The angles are supplementary of each other. A line that makes an angle with the positive direction x-axis and the angle is measured anti-clockwise, then θ is the inclination of the line.

Definition: If a line makes an angle θ with the positive direction x-axis, then tanθ is slope of the line.

The slope of a line is also denoted by the letter m,

Slope of a line when coordinates of any two points on the line are given

When two points are given as (x₁, y₁) and (x₂, y₂) the slope is

Conditions for Parallelism and Perpendicularity of Lines in Terms of Their Slopes

Parallel Lines

Let two lines l₁ and l₂ be parallel to each other. The slope of lines l₁ and l₂ are m₁ and m₂ The inclination of the lines l₁ and l₂ are α and β respectively. The diagram is shown below

Since the lines are parallel to each other so the angle of inclination also equal.

Hence, α=β

Taking tan both sides

tanα = tanβ and m₁ = m₂

The slope of line l₁ =The slope of line l₂

If the lines are parallel then the slope of the lines also equal.

Perpendicular Lines

Let two lines l₁ and l₂ be perpendicular to each other. The slope of lines l₁ and l₂ are m₁ and m₂. The inclination of the lines l₁ and l₂ are α and β respectively. The diagram is shown below

So, β= α+90°

Taking tan both sides

Two lines l1 and l2 are said to be perpendicular if m₁m₂ = -1

The Angle Between Two Lines

The inclination of two lines be θ₁ and θ₂ and θ₁θ₂ ≠ 90°

The slopes of the lines are m₁ = tanθ₁ and m₂ = tanθ₂

Assume that θ be the angle between the lines.

So,

Collinearity Of Three Points

Let three points be A(1,4), B(4,6), and C(10,10) lies on a same line.

The slope of the line that is passing through the points A(1,4) and B(4,6) is

The slope of the line that is passing through points B(4,6) and C(10,10) is

So, m_AB =m_BC =2/3

If the points lie on the same line then the slope of the line joining by any points is always the same.

Various Forms of the Equation of a Line

Horizontal and vertical lines

If a line is parallel to the x-axis and the distance of the line from the x-axis is b units. Then the equation of the line is

Either y=b or y =-b.

If a line is parallel to the y-axis and the distance of the line from the y-axis is a unit. Then the equation of the line is

Either x=a or x=-a

Point-Slope Form

Let a fixed point be (x₁,y₁) and an arbitrary point be (x,y).

Let m be the slope of the line.

Then

Two-point form

Let two points be (x₁,y₁) and (x₂,y₂) then

Slope-Intercept Form

Let the point on the y axis be (0,b) and m is the slope of the line

Then the formula is y=mx+b

Intercept - Form

Let the point on the coordinate axes be (a, 0) and (0, b)

Then the equation

Normal Form

General Equation Of A Line

The general equation goes by Ax+By+C=0

Different forms of Ax+By+C=0

Slope-intercept form

Intercept form

Distance of a Point from a Line

Let P(x₁, y₁) be a point that does not lie on the line Ax+By+C=0.

Then the distance of the point P(x₁, y₁) from the line is

Distance Between Two Parallel Lines

Suppose the equations of two parallel lines be Ax+By+C₁ = 0 and Ax+By+C₂ = 0

Then the distance between two parallel lines is

Significance of NCERT Class 11 Math Chapter 10 Notes

Class 11 Straight lines notes will be really helpful for the revision of the entire chapter and get a gist of the important topics covered in the notes. Also, Class 11 Math chapter 10 Notes is useful for getting a glance of Class 11 CBSE Syllabuses and also for national competitive exams like BITSAT, and JEE MAINS. Class 11 Maths chapter 10 notes pdf download can be used for getting a hard copy and to prepare for the exam.

Straight lines Class 11 notes pdf download: link

NCERT Class 11 Notes Chapter Wise.

Subject Wise NCERT Exemplar Solutions

• NCERT Exemplar Class 11 Solutions
• NCERT Exemplar Class 11 Maths
• NCERT Exemplar Class 11 Physics
• NCERT Exemplar Class 11 Chemistry
• NCERT Exemplar Class 11 Biology

Subject Wise NCERT Solutions

• NCERT Solutions for Class 11 Mathematics
• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 11 Physics

• NCERT Solutions for Class 11 Biology

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