# STRAIGHT LINES CLASS 11 MATHS

## Summary

*Slope (m) of a non-vertical line passing through the points (x1, y1) and (x2, y2) is given by m = \frac{y_2-y_1}{x_2-x_1}, x_1 \neq x_2*

*If a line makes an angle α with the positive direction of *x-axis*, then the slope of the line is given by m = tan α, α ≠ 90°*

Slope* of *horizontal* line is zero and *slope* of *vertical* line is undefined.*

*An acute angle (say θ) between lines L1 and L2 with slopes m1 and m2 is given by tan {\theta} = \left| \frac{m_2-m_1}{1+m_1 m_2} \right| , 1+m_1 m_2 \neq 0*

*Two lines are parallel if and only if their slopes are equal.*

*Two lines are perpendicular if and only if *product* of their slopes is –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 either y = a or y = – a.*

*Equation of the vertical line having distance b from the y-axis is either x = b or x = – b.*

*The point (x, y) lies on the line with slope m and through the fixed point (x0, y0), if and only if its coordinates satisfy the equation y - y_0 = m (x - x_0)*

*Equation of the line passing through the points (x1, y1) and (x2, y2) is given by y-y_1 = \frac{y_2-y_1}{x_2-x_1} (x-x_1)*

*The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c.*

*If a line with slope m makes x-intercept d. *Then equation* of the line is y = m (*x – d*).*

*Equation of a line making intercepts a and b on the x-and y-axis, respectively, is \frac{x}{a} + \frac{y}{b} = 1*

*The equation of the line having normal distance from origin p and *angle* between normal and the positive x-axis ω is given by x cos ω + y sin ω = *p .

*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.*

*The perpendicular distance (d) of a line Ax + By+ C = 0 from a point (x1, y1) is given by d = \frac{|A x_1 + B y_1 + C|}{\sqrt{A^2 + B^2}}*

*Distance between the parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0, is given by d = \frac{| C_1 - C_2 |}{\sqrt{A^2 + B^2 }}*

## Lecture - 1

- How to study Straight Lines (Coordinate Geometry)
- Arrangement of Straight Lines topic in NCERT
- Meaning and Definition of Equation through Animations
- How to find equation of any mathematical shape? Equation of Circle through Definition of Circle

## Lecture - 2

- Logical and Algebraical Meaning of Slope of a Line
- We can find slope of line using any two passing points of line with proof
- Relationship of Slope of line with angle made with positive direction of x-axis measured counter clockwise
- How to judge graphical representation of a line using slope

## Lecture - 3

- Derivation for angles between two lines using their slopes
- Condition of slopes if two lines are parallel
- Condition of slopes if two lines are perpendicular
- NCERT Exercise 10.1 (Q1 to Q7)

## Lecture - 4

- NCERT Exercise 10.1 (Q8 to Q14)
- Equation of line using area of triangle rule and collinear condition

## Lecture - 5

- Minimum information required to form any equation
- Point Slope form of Equation of a straight line
- NCERT Exercise 10.2 (Q1 to Q8)

## Lecture - 6

DERIVATIONS OF FORMULAS TO FIND EQUATION OF STRAIGHT LINES

- Two-point form
- NCERT Exercise 10.2 Question 7 using Two point form
- Slope intercept form and meaning of intercept
- NCERT Exercise 10.2 Question 5 using Slope intercept form
- NCERT Exercise 10.2 Question 6 using Slope intercept form
- Intercept form
- Normal Form of Straight Line
- NCERT Exercise 10.2 Question 8 using Normal Form

## Lecture - 9

- Standard Form of Equation of Straight Lines
- NCERT Exercise 10.3 (Q1 to Q3)

## Lecture - 10

- Derivation for Distance between a point and a straight line
- NCERT Exercise 10.3 (Q4 to Q6)

## Lecture - 11

- You will need to understand how to make equations and read information from equations before continuing
- NCERT Exercise 10.2 (Q7 to Q13)

## Lecture - 18

- Equation of Family of lines passing through the point of intersection of two lines with examples and animation
- NCERT Supplementary Exercise 10.4 (Q1 to Q4)

## Lecture - 19

- Purpose of coordinate axes
- Geometric Shapes follows “rigid body motion”
- All equations have two information related to geometric shapes
- Geometrical proof for benefits of shifting of origin
- Transformation or translation of axes has two parts : shifting of origin and rotation of axes
- Derivation for relation between new origin, old coordinate and new coordinate
- NCERT Supplementary Exercise 10.5 (Q1 & Q2)