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11M10

Straight Lines

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Distance Formula

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11M10.1

Slope of a Line

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Learning Objectives

What is Slope?

Finding Slope

Parallel and Perpendicular Lines

Angle Between Two Lines

Collinearity of Points

11M10.1 – Slope of a Line

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11M10.1

CV 0

Revision

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Recall Test

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Sol.

Using Section Formula,

Pause the video

(Time Duration : 2 minutes)

A

B

C

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11M10.1

CV 1

What is Slope?

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measured anti clockwise

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Conclusion :

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Sol.

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ConcepTest 1

Ready for a Challenge

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(NCERT Ex. 10.1- Q 7)

Sol.

Pause the video

(Time Duration : 2 minutes)

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11M10.1

CV 2

Finding Slope

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Slope of line when coordinates are given

M

R

S

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Sol.

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11M10.1

PSV 1

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(NCERT Ex. 10.1- Q 12)

Sol.

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11M10.1

CV 3

Parallel and Perpendicular Lines

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Condition for parallelism of lines in terms of their slopes

Inclinations are equal

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Condition for perpendicularity of lines in terms of their slopes

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Sol.

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11M10.1

PSV 2

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(NCERT Ex. 10.1- Q 6)

Sol.

A

B

C

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ConcepTest 2

Ready for a Challenge

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Sol.

Slope of line AB

Slope of line CD

Pause the video

(Time Duration : 3 minutes)

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11M10.1

CV 4

Angle Between Two Lines

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Sol.

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11M10.1

PSV 3

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Sol.

Case – 1

Case – 2

(NCERT Ex. 10.1- Q 11)

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ConcepTest 3

Ready for a Challenge

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Sol.

Case – 1

Case – 2

Pause the video

(Time Duration : 3 minutes)

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11M10.1

CV 5

Collinearity of Points

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A

C

B

If two lines having same slope pass through the common point, then two lines will coincide.

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Sol.

Slope of AB

Slope of BC

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11M10.1

PSV 4

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Sol.

(NCERT Ex. 10.1- Q 8)

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ConcepTest 4

Ready for a Challenge

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Sol.

(NCERT Ex. 10.1- Q 13)

Pause the video

(Time Duration : 3 minutes)

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Summary

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Reference Questions

NCERT Exercise 10.1 : 1, 2, 3, 4, 5, 9, 10, 14

Workbook : 1, 2, 3, 9, 10, 18

11M10.1 – Slope of a Line

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11M10.2

Forms of Equation of Line

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11M10.2 – Forms of Equation of Line

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11M10.2

CV 1

Horizontal and Vertical Lines

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Horizontal Line

Vertical Line

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Sol.

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11M10.2

CV 2

Point Slope Form

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By Definition of slope ,

Point Slope Form

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Sol.

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11M10.2

PSV 1

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Sol.

(NCERT Ex. 10.2- Q 4)

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ConcepTest 1

Ready for a Challenge

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Sol.

(NCERT Ex. 10.2- Q 10)

Pause the video

(Time Duration : 3 minutes)

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11M10.2

CV 3

Two Point Form

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By Definition of slope ,

Two Point Form

By Point slope form ,

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Sol.

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11M10.2

PSV 2

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Sol.

(NCERT Ex. 10.2 - Q 9)

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11M10.2

CV 4

Slope – Intercept Form

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By Point – Slope Form,

Equation of the line is

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Sol.

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11M10.2

CV 5

Intercept - Form

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b

a

By Two – Point Form, Equation of the line is

Intercept form

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Sol.

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11M10.2

PSV 3

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Sol.

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ConcepTest 2

Ready for a Challenge

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(NCERT Ex. 10.2 - Q 13)

Sol.

Pause the video

(Time Duration : 4 minutes)

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11M10.2

CV 6

Normal Form

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A

M

Length of perpendicular (normal) from the

origin to the line.

Normal Form

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Sol.

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ConcepTest 3

Ready for a Challenge

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Sol.

Pause the video

(Time Duration : 3 minutes)

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Summary

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Reference Questions

NCERT Exercise 10.2 : 1, 2, 3, 5, 6, 7, 8, 11, 12, 14, 15, 16, 17, 18, 19, 20

Workbook : 4, 5, 11, 12, 13, 14, 15, 17

11M10.2 – Various Forms of Equation of Line

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11M10.3

General Equation of Line

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Learning Objectives

What is General Equation of line?

Changing Equation of line into Slope – Intercept Form

Changing Equation of line into Intercept - Form

Changing Equation of line into Normal Form

Distance of a Point From a Line

Distance Between Two Parallel Lines

11M10.3 – General Equation of Line

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11M10.3

CV 1

What is General Equation of line?

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General Equation of Line

Example :-

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11M10.3

CV 2

Changing Equation of line into

Slope - Intercept Form

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General Equation of Line

Slope – Intercept Form

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Sol.

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11M10.3

PSV 1

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(NCERT Ex. 10.3 - Q 9)

Sol.

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11M10.3

CV 3

Changing Equation of line into

Intercept - Form

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General Equation of Line

Intercept - Form

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Sol.

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ConcepTest 1

Ready for a Challenge

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Pause the video

(Time Duration : 3 minutes)

Sol.

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11M10.3

CV 4

Changing Equation of line into

Normal Form

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General Equation of Line

Normal - Form

…(ii)

…(i)

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Sol.

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Sol.

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11M10.3

PSV 2

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Q.

Sol.

(NCERT Ex. 10.3 - Q 3(iii)

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11M10.3

CV 5

Distance of a Point from a Line

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11M10.3

PSV 3

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B

A

Sol.

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ConcepTest 2

Ready for a Challenge

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Sol.

Pause the video

(Time Duration : 3 minutes)

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11M10.3

CV 6

Distance Between Two Parallel Lines

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Sol.

(NCERT Ex. 10.3 - Q 6(i)

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11M10.3

PSV 4

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On solving equations (i) and (ii), we get

Sol.

foot of perpendicular

A

B

C

D

(NCERT Ex. 10.3 - Q 14)

Pause the video

(Time Duration : 2 minutes)

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ConcepTest 3

Ready for a Challenge

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Sol.

Pause the video

(Time Duration : 3 minutes)

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Sol.

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Summary

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Reference Questions

NCERT Exercise 10.3 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18

Workbook : 6, 7, 8, 16, 19, 20

11M10.3 – General Equation of Line