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NCERT Solutions for Exercise 10.1 Class 11 Maths Chapter 10 Straight Lines are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. In the earlier classes, you have already learned about the basics of two-dimensional coordinate geometry like the distance between two points, section formulae, coordinate axes, coordinate plane, plotting of points in a plane, etc. In the NCERT solutions for Class 11 maths ex 10.1, you will learn about the basic coordinate geometry like measuring the slope of the line when the coordinates of any two points on the line are given, conditions for parallelism and perpendicularity of lines in terms of their slopes, angle between two lines, colinearity of three points, etc.
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NCERT solutions for exercise 10.1 Class 11 Maths chapter 10 Straight Lines focuses straight line where you learn about the slope of lines, the angle between two lines. 11th class Maths exercise 10.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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**As per the CBSE Syllabus for 2023-24, this chapter has been renumbered as Chapter 9.
Access Straight Lines Class 11 Chapter 10 Exercise 10.1
Question:1 Draw a quadrilateral in the Cartesian plane, whose vertices are and . Also, find its area.
Answer:
Area of ABCD = Area of ABC + Area of ACD
Now, we know that the area of a triangle with vertices is given by
Therefore,
Area of triangle ABC
Similarly,
Area of triangle ACD
Now,
Area of ABCD = Area of ABC + Area of ACD
Answer:
it is given that it is an equilateral triangle and length of all sides is 2a
The base of the triangle lies on y-axis such origin is the midpoint
Therefore,
Coordinates of point A and B are respectively
Now,
Apply Pythagoras theorem in triangle AOC
Therefore, coordinates of vertices of the triangle are
Question:3(i) Find the distance between and when :
PQ is parallel to the -axis.
Answer:
When PQ is parallel to the y-axis
then, x coordinates are equal i.e.
Now, we know that the distance between two points is given by
Now, in this case
Therefore,
Therefore, the distance between and when PQ is parallel to y-axis is
Question:3(ii) Find the distance between and when :
PQ is parallel to the -axis.
Answer:
When PQ is parallel to the x-axis
then, x coordinates are equal i.e.
Now, we know that the distance between two points is given by
Now, in this case
Therefore,
Therefore, the distance between and when PQ is parallel to the x-axis is
Question:4 Find a point on the x-axis, which is equidistant from the points and .
Answer:
Point is on the x-axis, therefore, y coordinate is 0
Let's assume the point is (x, 0)
Now, it is given that the given point (x, 0) is equidistance from point (7, 6) and (3, 4)
We know that
Distance between two points is given by
Now,
and
Now, according to the given condition
Squaring both the sides
Therefore, the point is
Answer:
Mid-point of the line joining the points and . is
It is given that line also passes through origin which means passes through the point (0, 0)
Now, we have two points on the line so we can now find the slope of a line by using formula
Therefore, the slope of the line is
Answer:
It is given that point A(4,4) , B(3,5) and C(-1,-1) are the vertices of a right-angled triangle
Now,
We know that the distance between two points is given by
Length of AB
Length of BC
Length of AC
Now, we know that Pythagoras theorem is
Is clear that
Hence proved
Answer:
It is given that the line makes an angle of with the positive direction of -axis measured anticlockwise
Now, we know that
line makes an angle of with the positive direction of -axis
Therefore, the angle made by line with the positive x-axis is =
Now,
Therefore, the slope of the line is
Question:8 Find the value of for which the points and are collinear.
Answer:
Point is collinear which means they lie on the same line by this we can say that their slopes are equal
Given points are A(x,-1) , B(2,1) and C(4,5)
Now,
The slope of AB = Slope of BC
Therefore, the value of x is 1
Question:9 Without using the distance formula, show that points and are the vertices of a parallelogram.
Answer:
Given points are and
We know the pair of the opposite side are parallel to each other in a parallelogram
Which means their slopes are also equal
The slope of AB =
The slope of BC =
The slope of CD =
The slope of AD
=
We can clearly see that
The slope of AB = Slope of CD (which means they are parallel)
and
The slope of BC = Slope of AD (which means they are parallel)
Hence pair of opposite sides are parallel to each other
Therefore, we can say that points and are the vertices of a parallelogram
Question:10 Find the angle between the x-axis and the line joining the points and .
Answer:
We know that
So, we need to find the slope of line joining points (3,-1) and (4,-2)
Now,
Therefore, angle made by line with positive x-axis when measure in anti-clockwise direction is
Answer:
Let are the slopes of lines and is the angle between them
Then, we know that
It is given that and
Now,
Now,
Now,
According to which value of
Therefore,
Question:12 A line passes through and . If slope of the line is , show that .
Answer:
Given that A line passes through and and slope of the line is m
Now,
Hence proved
Question:13 If three points and lie on a line, show that
Answer:
Points and lie on a line so by this we can say that their slopes are also equal
We know that
Slope of AB =
Slope of AC =
Now,
Slope of AB = slope of AC
Now divide both the sides by hk
Hence proved
Answer:
Given point A(1985,92) and B(1995,97)
Now, we know that
Therefore, the slope of line AB is
Now, the equation of the line passing through the point (1985,92) and with slope = is given by
Now, in the year 2010 the population is
Therefore, the population in the year 2010 is 104.5 crore
Class 11th Maths chapter 10 exercise 10.1 consists of basic questions related to coordinate geometry like finding the distance between two points, slope of a line given the coordinates of two points on the line, checking the colinearity of three points, etc. There are five solved examples and few properties related to a straight line are given before the Class 11 Maths chapter 10 exercise 10.1 in the NCERT textbook. You must go through these properties and definitions of straight lines before solving the NCERt syllabus exercise problems.
Also Read| Straight Lines Class 11 Notes
Comprehensive Coverage: These 11th class maths exercise 10.1 answers cover all exercises and problems in Chapter 10.1 of the Class 11 Mathematics textbook.
Step-by-Step Approach: Ex 10.1 class 11 are presented in a clear, step-by-step format for easy understanding and problem-solving.
Clarity and Accuracy: The class 11 maths ex 10.1 solutions are precise and clear, ensuring a solid grasp of mathematical concepts and methods.
Conceptual Understanding: They focus on deepening understanding rather than memorization, promoting critical thinking.
Free Access: These class 11 ex 10.1 resources are typically available at no cost, making them accessible for self-study.
Supplementary Learning Tool: They can complement classroom instruction and aid exam preparation.
Homework and Practice: Useful for checking work, practicing problem-solving, and improving overall math skills.
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Happy learning!!!
The angle made by line l with the positive direction of x-axis and measured anticlockwise is called the inclination of the line 'l'.
The tan θ is called the slope or gradient of line 'l' where θ is the inclination of line 'l'.
Slope of line = tan 45 = 1
Condition for collinearity of points A, B, and C.
Slope of AB = Slope of BC
The slope of the x-axis is zero.
The slope of the y-axis is not defined.
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