Straight Lines class 11 Notes Mathematics

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Straight Lines class 11 Notes Mathematics

apter 10 Straight Lines Download CBSE class 11th revision notes for Chapter 10 Straight Lines class 11 Notes Mathematics in PDF format for free. Download revision notes for Straight Lines class 11 Notes Mathematics and score high in exams. These are the Straight Lines class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

Revision Notes for Class 11 Mathematics

CBSE Class 11 Mathematics Revision Notes Chapter-10 Straight Lines

1. Slope of a Line
2. Various Forms of the Equation of a Line
3. General Equation of a Line and Distance of a Point From a Line

First Degree Equation

Every first degree equation like $ax+by+c=0$ would be the equation of a straight line.

Slope of a line

• Slope (m) of a non-vertical line passing through the points $\left( {{\text{x}}_{1}}\text{ },\text{ }{{\text{y}}_{1}}\text{ } \right)$ and $\left( {{\text{x}}_{2}}\text{ },\text{ }{{\text{y}}_{2}} \right)$ is given by is given by   $\text{m }=\frac{{{y}_{1}}-{{y}_{2}}}{{{x}_{1}}-{{x}_{2}}}\text{= }$ ${{x}_{1}}\ne {{x}_{2}}$.
• If a line makes an angle á with the positive direction of x-axis, then the slope of the line is given by $\text{m =tan}\alpha \text{, }\alpha \ne \text{9}{{\text{0}}^{o}}\text{ }$
• Slope of horizontal line is zero and slope of vertical line is undefined.
• An acute angle (say θ) between lines ${{\text{L}}_{1}}\text{ and }{{\text{L}}_{2}}$ with slopes ${{\text{m}}_{1}}\text{ and }{{\text{m}}_{2}}$ is given by $\tan \theta =\left| \frac{{{m}_{2}}-{{m}_{1}}}{1+{{m}_{1}}{{m}_{2}}} \right|$, $1+{{m}_{1}}{{m}_{2}}\ne 0$
• Two lines are parallel if and only if their slopes are equal i.e., ${m_1} = {m_2}$
• Two lines are perpendicular if and only if product of their slopes is –1, i.e., ${m_1}.{m_2} = - 1$
• Three points A, B and C are collinear, if and only if slope of AB = slope of BC.
• Equation of the horizontal line having distance a from the x-axis is eithery = a  or y = – a.
• Equation of the vertical line having distance  b from the  y-axis is eitherx = b or x = – b.
• The point (x, y) lies on the line with slope m and through the fixed point $\left( {{\text{x}}_{o}},\text{ }{{\text{y}}_{0}}\text{ } \right),$ if and only if its coordinates satisfy the equation.

Various forms of equations of a line:

• Two points form: Equation of the line passing through the points $\left( {{\text{x}}_{1}},\text{ }{{\text{y}}_{1}} \right)$ and ($\text{(}{{\text{x}}_{2}},\text{ }{{\text{y}}_{2}})$ is given by $y-{{y}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}(x-{{x}_{1}})$
• Slope-Intercept form: The point (x, y) on the line with slope m and y-intercept c lies on the line if and only  if  $y=\text{mx +c}$.
• If a line with slope m makes  x-intercept  d. Then equation of the line  is $y=\text{m(x -d)}$.
• Intercept form: Equation of a line making intercepts  a and  b on the  x-and  y-axis, respectively, is  $\frac{x}{a}+\frac{y}{b}=1$.
• Normal form: The equation of the line having normal distance from origin p and angle between normal and the positive $\text{x}-\text{axis }\omega$ is given by $\text{ x cos}\omega \text{ +ysin }\omega =p$
• General Equation of a Line: Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.
• Working Rule for reducing general form into the normal form:

(i)     Shift constant ‘C’ to the R.H.S. and get $Ax+By=-C$

(ii)    If the R.H.S. is not positive, then make it positive by multiplying the whole equation by -1.

(iii)   Divide both sides of equation by $\sqrt {{{\rm{A}}^2} + {{\rm{B}}^2}}$.

The equation so obtained is in the normal form.

• Parametric Equation (Symmetric Form): ${{x - {x_1}} \over {\cos \theta }} = {{y - {y_1}} \over {\sin \theta }} = r$
• Equation of a line through origin: $y=mx$ or $y = x\tan \theta$.
• The perpendicular distance (d) of a line Ax + By+ C = 0 from a point $~~\left( {{\text{x}}_{1}},~{{\text{y}}_{1}} \right)$ is given  by $d=\frac{\left| A{{x}_{1}}+B{{y}_{1}}+C \right|}{\sqrt{{{A}^{2}}+{{B}^{2}}}}$
• Distance between the parallel lines $\text{Ax }+\text{ By }+\text{ }{{\text{C}}_{1}}$= 0 and = 0, is given by $d=\frac{\left| {{C}_{1}}-{{C}_{2}} \right|}{\sqrt{{{A}^{2}}+{{B}^{2}}}}$

CONCURRENT LINES

Three of more straight lines are said to be concurrent if they pass through a common point i.e., they meet at a point. Thus, if three lines are concurrent the point of intersection of two lines lies on the third line.

Condition of concurrency of three lines:

${a_1}\left( {{b_2}{c_3} - {b_3}{c_2}} \right) + {b_1}\left( {{c_2}{a_3} - {c_3}{a_2}} \right) + {c_1}\left( {{a_2}{b_3} - {a_3}{b_2}} \right) = 0$

EQUATIONS OF FAMILY OF LINES THROUGH THE INTERSECTION OF TWO LINES

${{\rm{A}}_1}x + {{\rm{B}}_1}y + {{\rm{C}}_1} + k\left( {{{\rm{A}}_2}x + {{\rm{B}}_2}y + {{\rm{C}}_2}} \right) = 0$

where $k$ is a constant and also called parameter.

This equation is of first degree of $x$ and $y$, therefore, it represents a family of lines.

DISTANCE BETWEEN TWO PARALLEL LINES

Working Rule to find the distance between two parallel lines:

(i)  Find the co-ordinates of any point on one of ht egiven line, preferably by putting  and $y=0$.

(ii) The perpendicular distance of this point from the other line is the required distance between the lines.

CBSE Class-11 Revision Notes and Key Points

Straight Lines class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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