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# NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.1 Straight Lines - PDF Download NCERT solutions for class 11 maths chapter 9 exercise 9.1 Straight Lines is based on slope of a line. You will learn the coordinates of a point in relation to the fixed point called the ‘Origin’. You can draw the shape by knowing the coordinates of the points in the vertices. You can also figure out its size by figuring out the length of its sides. This way, you can figure out the area or the perimeter of the shape. This exercise also includes essential questions based on finding a line’s slope. The problems can ask students to determine whether two lines are parallel or perpendicular to each other, as well as the angle between two intersecting lines.

## Topics Covered in Exercise 9.1 Class 11 Mathematics Questions

Ex 9.1 class 11 maths ch 9 covers topics like slope of a line, its applications and properties of straight lines. Check the detailed solutions given below.

 1 Slope of a Line 2 Slope of a line when coordinates of any two points on the line are given 3 Conditions for parallelism and perpendicularity of lines in terms of their slopes 4 Angle between two lines
1. Slope of a Line

A line in a coordinate plane forms two angles with the x-axis, which are supplementary to each other. The angle (say) θ made by the line l with positive direction of x-axis and measured anticlockwise is called the inclination of the line.

If θ is the inclination of a line l, then tan θ is called the slope or gradient of the line l.

The slope of a line whose inclination is 90° is not defined.

The slope of a line is denoted by m.

Thus, m = tan θ, θ ≠ 90°

1. Slope of a line when coordinates of any two points on the line are given

The slope m of the line through the points (x 1 , y1 ) and (x 2 , y2 ) is given by

m = $\frac{y_2-y_1}{x_2-x_1}$

1. Conditions for parallelism and perpendicularity of lines in terms of their slopes

Parallel Lines

In a coordinate plane,let non-vertical lines l and l2 have slopes m1 and m2 , respectively. Let their inclinations be α and β, respectively

If the line l is parallel to l2 , then their inclinations are equal

Hence α = β,

tan α = tan β and m1 = m2

slope of line l1 = slope of line l2

The slope of the lines is equal if the lines are parallel to each other.

Perpendicular Lines

If the lines l1 and l2 are perpendicular, then β = α + 90°. Therefore, tan β = tan (α + 90°)

if m1 m2 = – 1,

tan α tan β = – 1

Then tan α = – cot β = tan (β + 90°) or tan (β – 90°)

Therefore, α and β differ by 90°.

Thus, lines l1 and l2 are perpendicular to each other.

Two nonvertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

1. Angle between two lines

The inclination of two lines l1, l2 be α1 and α2 and α1α2≠  90°

The slopes of the lines are m1 = tan1 and m2 = tanα2

Suppose θ is the angle between the lines

tan θ = tan (α2 – α1 ) = $\frac{\tan a_2-\tan a_1}{1+\tan a_1 \tan a_2}=\frac{m_2-m_1}{1+m_1 m_2}$     , as 1 + m1m2 ≠ 0

## Tips for Solving Exercise 9.1 Class 11 Chapter 9 Straight Lines

We suggest the students have the right orientation to comprehend the questions in NCERT solutions class 11 maths chapter 9 ex 9.1. Here, our expert teachers of mathematics have provided useful tips and tricks to solve exercise 9.1 questions.

1. This exercise involves the utilization of multiple formulas, so it is recommended that students create a formula chart to gain a better comprehension of the concepts.

2. Students must solve problems which are provided in NCERT solutions by eSaral. By solving these problems, students will find the straight line slope and how to graphically interpret the answer.

3. Before solving ex 9.1 questions students must solve examples given before the exercise to be well-versed with the questions and concepts.

## Importance of Solving Ex 9.1 Class 11 Maths Chapter 9 Straight Lines

It is essential for students to solve exercise questions to get the most of the topics included in the chapter. Here, we have covered the most important benefits of solving questions of ex 9.1 class 11 maths chapter 9 straight lines.

1. Solving ex 9.1 questions will provide you the fundamentals of slope of a line and its applications that will give you conceptual understanding of concepts.

3. Ex 9.1 class 11 maths chapter 9 has questions in different levels that will provide you a clear and precise understanding of every concept. This will build your self-confidence in the examination.

4. By revising the concepts and important questions of ex 9.1 class 11 maths ch 9 solutions, you can improve your speed and accuracy of solving problems.

Question 1. What is the inclination of a line 'l' in NCERT solutions class 11 maths chapter 9?

Answer 1. The angle made by the line l with positive direction of x-axis and measured anticlockwise is called the inclination of the line.

Question 2. What do you mean by slope of a line?

Answer 2. If θ is the inclination of a line l, then tan θ is called the slope or gradient of the line l.  