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 - 7

• NCERT Exercise 10.2 (Q9 to Q13)

Lecture - 8

• NCERT Exercise 10.2 (Q14 to Q20)

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 - 12

• NCERT Exercise 10.3 (Q14 to Q18)

Lecture - 13

• NCERT Exercise 10.3 Question 11
• Miscellaneous Exercise (Q1 to Q7)

Lecture - 14

• Miscellaneous Exercise (Q8 to Q12)

Lecture - 15

• NCERT Miscellaneous Exercise (Q14 to Q19)

Lecture - 16

• NCERT Miscellaneous Exercise (Q20 to Q24)

Lecture - 17

• Miscellaneous Exercise (Q8 to Q12)

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)