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Edited By Vishal kumar | Updated on Nov 09, 2023 11:49 AM IST

In the previous exercise, you have already learned about finding the minimum distance between two points, the slope of the line given two coordinate points on the line, the angles between two lines, etc. In this article, you will get NCERT syllabus for Class 11 Maths chapter 10 exercise 10.2 where you will learn about the various forms of the equation of the line. Equations of the coordinate axis, equation of the line in the point-slope form, equation of the line in the two-point form, equation of the line in the slope-intersect form, equation of the line in intersect form, equation of the line in the normal form are also covered in the NCERT book Class 11 Maths chapter 10 exercise 10.2 solutions.

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- NCERT Solutions for Class 11 Maths Chapter 10: Straight Lines Exercise 10.2- Download Free PDF
- NCERT Solutions for Class 11 Maths Chapter 10– Straight Lines Exercise 10.2
- More About NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.2:-
- Benefits of NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.2:-
- Key Features of Exercise 10.2 Class 11 Maths Solutions
- NCERT Solutions of Class 11 Subject Wise
- NCERT Solutions for Class 11 Maths
- Subject Wise NCERT Exampler Solutions

Exercise 10.2 Class 11 Maths is a very useful exercise in two-dimensional geometry and very important for the CBSE exam as well. If you have basic knowledge of two-dimensional geometry, you will easily grasp the concepts of Class 11 Maths chapter 10 exercise 10.2. Also, check NCERT Solutions link if you are looking for NCERT solutions explained in a detailed manner.

**Also, see**

****As per the CBSE Syllabus for 2023-24, this chapter has been renumbered as Chapter 9.**

**Access Straight Lines Class 11 Chapter 10**** Exercise: 10.2**

Question:1 Find the equation of the line which satisfy the given conditions:

Write the equations for the -and -axes.

Answer:

Equation of x-axis is y = 0

and

Equation of y-axis is x = 0

Question:2 Find the equation of the line which satisfy the given conditions:

Passing through the point with slope .

Answer:

We know that , equation of line passing through point and with slope m is given by

Now, equation of line passing through point (-4,3) and with slope is

Therefore, equation of the line is

Question:3 Find the equation of the line which satisfy the given conditions:

Passing through with slope .

Answer:

We know that the equation of the line passing through the point and with slope m is given by

Now, the equation of the line passing through the point (0,0) and with slope m is

Therefore, the equation of the line is

Question:4 Find the equation of the line which satisfy the given conditions:

Passing through and inclined with the x-axis at an angle of .

Answer:

We know that the equation of the line passing through the point and with slope m is given by

we know that

where is angle made by line with positive x-axis measure in the anti-clockwise direction

Now, the equation of the line passing through the point and with slope is

Therefore, the equation of the line is

Question:5 Find the equation of the line which satisfy the given conditions:

Intersecting the -axis at a distance of units to the left of origin with slope .

Answer:

We know that the equation of the line passing through the point and with slope m is given by

Line Intersecting the -axis at a distance of units to the left of origin which means the point is (-3,0)

Now, the equation of the line passing through the point (-3,0) and with slope -2 is

Therefore, the equation of the line is

Question:6 Find the equation of the line which satisfy the given conditions:

Intersecting the -axis at a distance of units above the origin and making an angle of with positive direction of the x-axis.

Answer:

We know that , equation of line passing through point and with slope m is given by

Line Intersecting the y-axis at a distance of 2 units above the origin which means point is (0,2)

we know that

Now, the equation of the line passing through the point (0,2) and with slope is

Therefore, the equation of the line is

Question:7 Find the equation of the line which satisfy the given conditions:

Passing through the points and .

Answer:

We know that , equation of line passing through point and with slope m is given by

Now, it is given that line passes throught point (-1 ,1) and (2 , -4)

Now, equation of line passing through point (-1,1) and with slope is

Question:8 Find the equation of the line which satisfy the given conditions:

Perpendicular distance from the origin is units and the angle made by the perpendicular with the positive -axis is .

Answer:

It is given that length of perpendicular is 5 units and angle made by the perpendicular with the positive -axis is

Therefore, equation of line is

In this case p = 5 and

Therefore, equation of the line is

Question:9 The vertices of are and . Find equation of the median through the vertex .

Answer:

The vertices of are and

Let m be RM b the median through vertex R

Coordinates of M (x, y ) =

Now, slope of line RM

Now, equation of line passing through point and with slope m is

equation of line passing through point (0 , 2) and with slope is

Therefore, equation of median is

Question:10 Find the equation of the line passing through and perpendicular to the line through the points and .

Answer:

It is given that the line passing through and perpendicular to the line through the points and

Let the slope of the line passing through the point (-3,5) is m and

Slope of line passing through points (2,5) and (-3,6)

Now this line is perpendicular to line passing through point (-3,5)

Therefore,

Now, equation of line passing through point and with slope m is

equation of line passing through point (-3 , 5) and with slope 5 is

Therefore, equation of line is

Answer:

Co-ordinates of point which divide line segment joining the points and in the ratio is

Let the slope of the perpendicular line is m

And Slope of line segment joining the points and is

Now, slope of perpendicular line is

Now, equation of line passing through point and with slope m is

equation of line passing through point and with slope is

Therefore, equation of line is

Answer:

Let (a, b) are the intercept on x and y-axis respectively

Then, the equation of the line is given by

Intercepts are equal which means a = b

Now, it is given that line passes through the point (2,3)

Therefore,

therefore, equation of the line is

Question:13 Find equation of the line passing through the point and cutting off intercepts on the axes whose sum is .

Answer:

Let (a, b) are the intercept on x and y axis respectively

Then, the equation of line is given by

It is given that

a + b = 9

b = 9 - a

Now,

It is given that line passes through point (2 ,2)

So,

case (i) a = 6 b = 3

case (ii) a = 3 , b = 6

Therefore, equation of line is 2x + y = 6 , x + 2y = 6

Answer:

We know that

Now, equation of line passing through point (0 , 2) and with slope is

Therefore, equation of line is -(i)

Now, It is given that line crossing the -axis at a distance of units below the origin which means coordinates are (0 ,-2)

This line is parallel to above line which means slope of both the lines are equal

Now, equation of line passing through point (0 , -2) and with slope is

Therefore, equation of line is

Question:15 The perpendicular from the origin to a line meets it at the point , find the equation of the line.

Answer:

Let the slope of the line is m

and slope of a perpendicular line is which passes through the origin (0, 0) and (-2, 9) is

Now, the slope of the line is

Now, the equation of line passes through the point (-2, 9) and with slope is

Therefore, the equation of the line is

Answer:

It is given that

If then

and If then

Now, if assume C along x-axis and L along y-axis

Then, we will get coordinates of two points (20 , 124.942) and (110 , 125.134)

Now, the relation between C and L is given by equation

Which is the required relation

Answer:

It is given that the owner of a milk store sell

980 litres milk each week at

and litres of milk each week at

Now, if we assume the rate of milk as x-axis and Litres of milk as y-axis

Then, we will get coordinates of two points i.e. (14, 980) and (16, 1220)

Now, the relation between litres of milk and Rs/litres is given by equation

Now, at he could sell

He could sell 1340 litres of milk each week at

Question:18 is the mid-point of a line segment between axes. Show that equation of the line is .

Answer:

Now, let coordinates of point A is (0 , y) and of point B is (x , 0)

The,

Therefore, the coordinates of point A is (0 , 2b) and of point B is (2a , 0)

Now, slope of line passing through points (0,2b) and (2a,0) is

Now, equation of line passing through point (2a,0) and with slope is

Hence proved

Question:19 Point divides a line segment between the axes in the ratio . Find equation of the line.

Answer:

Let the coordinates of Point A is (x,0) and of point B is (0,y)

It is given that point R(h , k) divides the line segment between the axes in the ratio

Therefore,

R(h , k)

Therefore, coordinates of point A is and of point B is

Now, slope of line passing through points and is

Now, equation of line passing through point and with slope is

Therefore, the equation of line is

Question:20 By using the concept of equation of a line, prove that the three points and are collinear.

Answer:

Points are collinear means they lies on same line

Now, given points are and

Equation of line passing through point A and B is

Therefore, the equation of line passing through A and B is

Now, Equation of line passing through point B and C is

Therefore, Equation of line passing through point B and C is

When can clearly see that Equation of line passing through point A nd B and through B and C is the same

By this we can say that points and are collinear points

Class 11th Maths chapter 10 exercise 10.2 consists of questions related to finding equations of lines in various forms like two-point form, point-slope form, etc. Equation of line is the most basic as well as very important concept of two-dimensional geometry. There are few solved examples and some important concepts given before the Class 11 Maths chapter 10 exercise 10.2. You must go through the theory related equations of lines given before solving the exercise 10.2 Class 11 Maths problems.

**Also Read| **Straight Lines Class 11 Notes

- Exercise 10.2 Class 11 maths is very important to understand two-dimensional geometry.
- You must try to solve Class 11 Maths chapter 10 exercise 10.2 problems by yourself.
- Class 11 Maths chapter 10 exercise 10.2 solutions are here to assist you if you face any difficulty while solving them.

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Download EBook**Complete Exercise Coverage:**These 11th class maths exercise 10.2 answers encompass all exercises and problems found in Chapter 10.2 of the Class 11 Mathematics textbook.**Step-by-Step Approach:**The ex 10.2 class 11 solutions are presented in a clear, step-by-step format, aiding students in understanding and applying problem-solving methods effectively.**Clarity and Precision:**The class 11 maths ex 10.2 solutions are written with clarity and precision, ensuring that students can easily comprehend the mathematical concepts and techniques required for successful problem-solving.**Correct Mathematical Notation:**Appropriate mathematical notations and terminology are used, helping students become proficient in the language of mathematics.**Emphasis on Conceptual Understanding:**The class 11 ex 10.2 solutions aim to foster a deep understanding of mathematical concepts, encouraging critical thinking and problem-solving skills.**Free Accessibility:**Typically, these ex 10.2 class 11 solutions are available free of charge, making them an accessible and valuable resource for self-study.**Supplementary Learning Tool:**These class 11 ex 10.2 solutions can be used as supplementary resources to complement classroom instruction and support students in exam preparation.**Homework and Practice:**Students can utilize these solutions to cross-verify their work, practice problem-solving, and enhance their overall performance in mathematics.

**Happy learning!!!**

1. Write the equation of line passing through points (0,0) and (1,1) ?

Equation of line passing through points (0,0) and (1,1) => y-0 = (1-0)/(1-0) ( x -0)

y = x

2. Write the equation of line passing through points (0,0) and slope is 2 ?

Equation of line passing through points (0,0) and slope is 2 => y = 2x + c

Line is passing through (0,0) => 0 = 0 +c => c=0

Equation of the line => y = 2x

3. Write the equation of line parallel to x-axis and passing through (2,4) ?

The equation of line parallel to x-axis=> y = c

Line is passing through (2,4) => c =4

Equation of the line => y = 4

4. Write the equation of line parallel to y-axis and passing through (2,4) ?

The equation of line parallel to y-axis=> x = c

Line is passing through (2,4) => c =2

Equation of the line => x = 2

5. Write the equation of x-axis ?

Equation of x-axis => y = 0

6. Write the equation of y-axis ?

Equation of y-axis => x = 0

Sep 06, 2024

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