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RD Sharma Solutions for Class 9 Maths Chapter 11 - Coordinate Geometry
By Swati Singh
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Updated on 29 Apr 2025, 15:40 IST
In Chapter 11 of RD Sharma Solutions for Class 9 Maths, students will explore the fundamentals of coordinate geometry. This chapter covers topics such as the Cartesian plane, coordinates of a point, terminology related to the coordinate system, notations, and plotting points on the plane.
Students can easily access RD Sharma Solutions through the provided links, which will assist them in solving problems from the textbook. The solutions are designed by IL subject experts, offering clear and detailed explanations for each question.
These solutions, updated for the 2025-26 exams, help students strengthen their mathematical skills. The RD Sharma Solutions are available for free online, and students can view them or download them as PDFs for future reference. For effective exam preparation, it’s recommended that students solve all problems in the RD Sharma textbook, using the solutions provided to guide their learning.
RD Sharma Solution for Class 9 Chapter 11 - Download PDF
Here are the RD Sharma Solutions Class 9 Maths Chapter 11 Coordinate Geometry Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
RD Sharma Solution for Class 9 Chapter 11 - Question with Answers
1. What is coordinate geometry?
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Answer: Coordinate geometry is the branch of mathematics that deals with the study of geometric shapes using a coordinate system, specifically the Cartesian plane, where points are defined by their distance from two perpendicular axes.
2. What are the coordinates of a point?
Answer: The coordinates of a point are a pair of values that represent its position on the Cartesian plane. The first value is the x-coordinate (horizontal position), and the second value is the y-coordinate (vertical position).
3. What is the Cartesian plane?
Answer: The Cartesian plane is a two-dimensional plane formed by two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). This plane is used to plot points based on their coordinates.
4. What are the four quadrants of the Cartesian plane?
Answer: The Cartesian plane is divided into four quadrants:
First quadrant: Both x and y are positive.
Second quadrant: x is negative, and y is positive.
Third quadrant: Both x and y are negative.
Fourth quadrant: x is positive, and y is negative.
5. What is the origin in the coordinate plane?
Answer: The origin is the point where the x-axis and y-axis intersect, represented by the coordinates (0, 0).
6. What does the x-coordinate represent?
Answer: The x-coordinate represents the horizontal distance of a point from the y-axis. It tells us how far left or right the point is from the origin.
7. What does the y-coordinate represent?
Answer: The y-coordinate represents the vertical distance of a point from the x-axis. It tells us how far up or down the point is from the origin.
8. What are the coordinates of the point on the x-axis?
Answer: Any point on the x-axis has a y-coordinate of zero. Its coordinates are in the form (x, 0), where x is any value.
9. What are the coordinates of the point on the y-axis?
Answer: Any point on the y-axis has an x-coordinate of zero. Its coordinates are in the form (0, y), where y is any value.
10. What is the distance formula in coordinate geometry?
Answer: The distance formula calculates the distance between two points on the Cartesian plane. It is derived from the Pythagorean theorem and involves the difference in the x-coordinates and y-coordinates of the points.
11. How do you find the midpoint of a line segment in coordinate geometry?
Answer: The midpoint of a line segment joining two points is found by averaging the x-coordinates and y-coordinates of the points. The formula for the midpoint is ((x1 + x2)/2, (y1 + y2)/2).
12. What are the applications of coordinate geometry?
Answer: Coordinate geometry is used in various fields such as computer graphics, navigation, physics, engineering, and architecture, where it helps in analyzing shapes, distances, and angles.
13. How do you plot a point on the Cartesian plane?
Answer: To plot a point on the Cartesian plane, start at the origin (0, 0), move along the x-axis according to the x-coordinate, and then move vertically according to the y-coordinate to locate the point.
14. What is the significance of the slope of a line in coordinate geometry?
Answer: The slope of a line measures its steepness and direction. It is calculated as the ratio of the change in y to the change in x between two points on the line.
15. What is the equation of a straight line in coordinate geometry?
Answer: The equation of a straight line in coordinate geometry is typically written in the form y = mx + c, where m is the slope and c is the y-intercept.
16. What is the slope of a horizontal line?
Answer: The slope of a horizontal line is zero because there is no vertical change between any two points on the line.
17. What is the slope of a vertical line?
Answer: The slope of a vertical line is undefined because the change in the x-coordinate is zero, which leads to division by zero.
18. How do you find the area of a triangle in coordinate geometry?
Answer: The area of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3) can be calculated using the formula: Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.
19. What is the equation of a line through two given points?
Answer: The equation of a line through two points (x1, y1) and (x2, y2) can be found using the slope formula m = (y2 - y1) / (x2 - x1) and the point-slope form of a line equation.
20. What is a linear equation in two variables?
Answer: A linear equation in two variables is an equation that represents a straight line on the Cartesian plane. It is typically written in the form Ax + By + C = 0, where A, B, and C are constants.
21. What is the slope-intercept form of a line?
Answer: The slope-intercept form of a line is y = mx + c, where m is the slope of the line and c is the y-intercept (the point where the line crosses the y-axis).
22. How do you determine if two lines are parallel?
Answer: Two lines are parallel if they have the same slope. In the equation of a line y = mx + c, if the slopes (m) of two lines are equal, the lines are parallel.
23. How do you determine if two lines are perpendicular?
Answer: Two lines are perpendicular if the product of their slopes is -1. If the slopes of two lines are m1 and m2, then m1 * m2 = -1 for the lines to be perpendicular.
24. What is the distance between a point and a line?
Answer: The distance between a point and a line is the shortest distance, which is measured along the perpendicular from the point to the line.
25. How do you find the slope of a line from its equation?
Answer: In the slope-intercept form y = mx + c, the slope of the line is the coefficient of x, which is m.
26. What does the y-intercept of a line represent?
Answer: The y-intercept of a line is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.
27. How do you find the midpoint of a line segment joining two points?
Answer: The midpoint of a line segment is found by averaging the x-coordinates and y-coordinates of the two points. The formula is ((x1 + x2)/2, (y1 + y2)/2).
28. What is the significance of the equation of a line?
Answer: The equation of a line represents the relationship between the x and y coordinates of every point on that line. It helps us understand the direction, slope, and position of the line on the Cartesian plane.
29. How can coordinate geometry be used in real life?
Answer: Coordinate geometry is used in navigation, engineering, computer graphics, architecture, and many other fields to solve problems involving distances, angles, and shapes.
30. What is the formula for the distance between two points in the coordinate plane?
Answer: The distance between two points (x1, y1) and (x2, y2) is calculated using the formula: Distance = √[(x2 - x1)² + (y2 - y1)²].
31. How do you find the area of a quadrilateral in coordinate geometry?
Answer: The area of a quadrilateral with vertices at (x1, y1), (x2, y2), (x3, y3), and (x4, y4) can be calculated using the formula: Area = 1/2 * |x1y2 + x2y3 + x3y4 + x4y1 - (y1x2 + y2x3 + y3x4 + y4x1)|.
32. What is the equation of a vertical line?
Answer: The equation of a vertical line is of the form x = a, where "a" is the constant x-coordinate for all points on the line.
33. What is the equation of a horizontal line?
Answer: The equation of a horizontal line is of the form y = b, where "b" is the constant y-coordinate for all points on the line.
34. How do you find the equation of a line passing through two points?
Answer: To find the equation of a line passing through two points, first calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Then, use the point-slope form of the equation to write the equation of the line.
35. What is the slope of the line joining two points?
Answer: The slope of the line joining two points (x1, y1) and (x2, y2) is calculated as (y2 - y1) / (x2 - x1).
36. How do you find the equation of a line using its slope and a point?
Answer: To find the equation of a line, use the point-slope form of the equation: y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point on the line.
37. What is the formula for finding the length of a line segment?
Answer: The length of a line segment joining two points (x1, y1) and (x2, y2) is given by the formula: Length = √[(x2 - x1)² + (y2 - y1)²].
38. How do you calculate the slope between two points?
Answer: The slope between two points is calculated as the difference in y-coordinates divided by the difference in x-coordinates: (y2 - y1) / (x2 - x1).
39. What is the midpoint formula for two points?
Answer: The midpoint formula is ((x1 + x2)/2, (y1 + y2)/2), which gives the point exactly halfway between two other points.
40. How do you determine the equation of a line parallel to a given line?
Answer: To determine the equation of a line parallel to a given line, use the same slope as the given line and a new point. The equation will be in the form y - y1 = m(x - x1).
Importance of RD Sharma Solutions for Class 9 Maths Chapter 11 - Coordinate Geometry
1. Clear Understanding of Basic Concepts: RD Sharma Solutions for Chapter 11 on Coordinate Geometry are designed to help students build a strong foundation in understanding key concepts such as the Cartesian plane, coordinates, distance between points, and the relationship between geometric shapes and coordinates. This clarity is essential for tackling more advanced topics in mathematics.
2. Step-by-Step Problem Solving: The solutions provided are step-by-step, making it easier for students to grasp the logical flow of solving problems. By following these solutions, students can understand the methods and reasoning behind every calculation, which enhances their problem-solving skills.
3. Real-World Applications: Coordinate Geometry has a wide range of applications in real life, such as navigation, engineering, architecture, computer graphics, and physics. RD Sharma Solutions help students understand how these concepts are applied in practical situations, making the topic more relevant and interesting.
4. Concept Reinforcement Through Practice: The solutions are structured around the exercises in the RD Sharma textbook, offering ample practice for students. Regular practice is key to mastering coordinate geometry and ensures that students can solve a variety of problems efficiently.
5. Preparation for Exams: Coordinate geometry is a crucial topic for Class 9 exams and future competitive exams like JEE. RD Sharma Solutions provide a comprehensive approach to preparing for exams by ensuring that students are well-versed in key concepts and techniques, boosting their confidence for the final exams.
6. Visualizing Geometric Concepts: One of the strengths of RD Sharma Solutions is that they allow students to visualize geometric concepts using the Cartesian plane. This makes abstract concepts like distance between points, midpoint, and slope much easier to understand and apply.
7. Clear Explanations by Experts: The solutions are prepared by subject experts who offer detailed explanations for each concept and problem. This helps students understand even the most difficult problems and learn to approach them in a structured manner.
8. Helps in Developing Critical Thinking: By working through the problems in RD Sharma Solutions, students are encouraged to think critically and analytically. This develops their ability to break down complex problems into smaller, manageable steps, improving their overall mathematical thinking.
9. Free Access for Students: RD Sharma Solutions are available for free online, allowing students to access them anytime. This makes it easy for students to study at their own pace and refer to the solutions whenever needed.
10. Building a Strong Foundation for Future Learning: Mastering coordinate geometry in Class 9 sets the stage for more advanced topics in higher grades, including algebra, calculus, and trigonometry. The skills learned here will help students in all future mathematical studies
FAQs on RD Sharma Solutions for Class 9 Maths Chapter 11
What is the meaning of quadrants according to RD Sharma Solutions for Class 9 Maths Chapter 11?
According to RD Sharma Solutions for Chapter 11, the Cartesian plane is divided into four quadrants by the x-axis and y-axis. The quadrants are numbered in a counter-clockwise direction, starting from the top-right. The first quadrant has both positive x and y values, the second has a negative x and positive y, the third has both negative x and y values, and the fourth has a positive x and a negative y.
How many exercise questions are there in RD Sharma Solutions for Class 9 Maths Chapter 11?
RD Sharma Solutions for Class 9 Maths Chapter 11 contains multiple exercises that provide a variety of problems to practice. Typically, the chapter includes three to four exercises, covering different topics of coordinate geometry, including distance between points, plotting points, and more.
What are the main topics covered in RD Sharma Solutions for Class 9 Maths Chapter 11?
The main topics covered in Chapter 11 include:
The Cartesian plane and its four quadrants.
Coordinates of points on the plane.
Distance formula for finding the distance between two points.
Midpoint formula for finding the midpoint of a line segment.
Application of coordinate geometry in solving problems.
Is it worthy to follow RD Sharma Solutions Class 9 Maths Chapter 11?
Yes, RD Sharma Solutions for Chapter 11 are very beneficial. They provide clear, step-by-step explanations for all problems and concepts related to coordinate geometry. The solutions are designed to enhance your understanding and improve your problem-solving skills, making it a valuable resource for exam preparation.
How many questions are there in RD Sharma Solutions for Class 9 Maths Chapter 11?
RD Sharma Solutions for Chapter 11 contains several questions in each exercise, ranging from basic to advanced level. Typically, there are around 15 to 20 questions in each exercise, with varying difficulty levels to help students grasp the concepts thoroughly.