CBSE Class 10 Mathematics (2026–27)
Chapter 7: Coordinate Geometry
20 Important Questions and Answers
Q1. What is a coordinate plane? Explain its parts.
Answer:
A coordinate plane is a two-dimensional surface formed by two perpendicular number lines called the x-axis and y-axis. The point where these axes intersect is called the origin (0, 0). The x-axis represents horizontal distances, while the y-axis represents vertical distances. These axes divide the plane into four regions called quadrants. Points on the coordinate plane are represented by ordered pairs (x, y), where x indicates the horizontal position and y indicates the vertical position. Coordinate geometry helps us locate points accurately and study geometric figures using algebraic methods. It is widely used in mathematics, engineering, navigation, and computer graphics.
Q2. What are the coordinates of the origin and points lying on the axes?
Answer:
The origin is the point where the x-axis and y-axis intersect, and its coordinates are (0, 0). Any point lying on the x-axis has a y-coordinate equal to zero. For example, (4, 0) and (−3, 0) lie on the x-axis. Similarly, any point lying on the y-axis has an x-coordinate equal to zero. Examples are (0, 5) and (0, −2). Points on the axes are important because they help in understanding the position of other points on the coordinate plane. They also serve as references for plotting and measuring distances in coordinate geometry.
Q3. Define an ordered pair. Why is the order important?
Answer:
An ordered pair is a pair of numbers written in the form (x, y), where x represents the horizontal distance from the y-axis and y represents the vertical distance from the x-axis. The order of the numbers is very important because changing the order changes the location of the point. For example, the points (3, 5) and (5, 3) are different points on the coordinate plane. The first number always indicates movement along the x-axis, while the second number indicates movement along the y-axis. Ordered pairs help in locating and identifying points accurately in coordinate geometry.
Q4. Explain the four quadrants of the coordinate plane.
Answer:
The x-axis and y-axis divide the coordinate plane into four quadrants. The first quadrant lies in the upper-right region, where both x and y coordinates are positive. In the second quadrant, x is negative and y is positive. The third quadrant has both x and y negative. In the fourth quadrant, x is positive and y is negative. The quadrants are numbered in an anti-clockwise direction starting from the first quadrant. Understanding quadrants helps in determining the position and signs of coordinates of any point. This concept is essential for plotting points correctly on a graph.
Q5. In which quadrant does the point (−4, 5) lie? Explain.
Answer:
The point (−4, 5) lies in the second quadrant. To determine the quadrant, we examine the signs of the coordinates. The x-coordinate is −4, which is negative, and the y-coordinate is 5, which is positive. In coordinate geometry, any point with a negative x-coordinate and a positive y-coordinate lies in the second quadrant. This method can be used for identifying the location of any point on the coordinate plane. Knowing the quadrant helps in plotting points correctly and understanding their relative positions with respect to the axes and the origin.
Q6. How do you plot a point on a graph paper?
Answer:
To plot a point on graph paper, first locate the origin where the x-axis and y-axis intersect. Consider the point (3, 4). Move 3 units to the right along the x-axis because the x-coordinate is positive. Then move 4 units upward parallel to the y-axis because the y-coordinate is positive. Mark the point and label it. If a coordinate is negative, move left for negative x-values and downward for negative y-values. Plotting points accurately is important because it helps represent geometric figures and solve problems involving coordinate geometry effectively.
Q7. What is the significance of the x-axis and y-axis?
Answer:
The x-axis and y-axis are the two reference lines that form the coordinate plane. The x-axis is a horizontal line used to measure distances left or right from the origin. The y-axis is a vertical line used to measure distances above or below the origin. Together, they help determine the exact position of any point using coordinates. These axes divide the plane into four quadrants and serve as the basis for graphing mathematical relationships. Understanding the role of the axes is essential for plotting points, interpreting graphs, and solving coordinate geometry problems.
Q8. Determine the quadrant of the point (6, −2).
Answer:
The point (6, −2) lies in the fourth quadrant. To identify the quadrant, observe the signs of the coordinates. The x-coordinate is positive, indicating that the point lies to the right of the y-axis. The y-coordinate is negative, indicating that the point lies below the x-axis. A point with a positive x-coordinate and a negative y-coordinate always lies in the fourth quadrant. Understanding the signs of coordinates helps students quickly identify the location of points and plot them correctly on the coordinate plane.
Q9. Why is coordinate geometry useful in real life?
Answer:
Coordinate geometry has many practical applications in daily life. It is used in navigation systems such as GPS to determine exact locations. Engineers and architects use coordinate geometry to design buildings, roads, and bridges. Computer graphics and video game developers use coordinates to place objects accurately on screens. Scientists use coordinate systems to represent data and study motion. Coordinate geometry helps convert geometric problems into algebraic equations, making them easier to solve. Thus, it plays an important role in technology, mapping, construction, and scientific research.
Q10. Explain the position of a point on the y-axis.
Answer:
A point lying on the y-axis has an x-coordinate equal to zero. This is because the y-axis itself represents all points where there is no horizontal movement from the origin. For example, the points (0, 4), (0, −7), and (0, 0) all lie on the y-axis. The y-coordinate may be positive, negative, or zero depending on the position of the point. Points above the origin have positive y-values, while points below the origin have negative y-values. Understanding this concept helps students identify and plot points accurately on graphs.
Q11. Explain the position of a point on the x-axis.
Answer:
A point on the x-axis has a y-coordinate equal to zero because there is no vertical movement from the x-axis. Examples include (5, 0), (−8, 0), and (0, 0). The x-coordinate may be positive, negative, or zero depending on the location of the point. Positive x-values lie to the right of the origin, while negative x-values lie to the left. The x-axis is an important reference line used for measuring horizontal distances. Understanding points on the x-axis is essential for graphing and solving problems in coordinate geometry.
Q12. Locate the point (−3, −4) and identify its quadrant.
Answer:
The point (−3, −4) lies in the third quadrant. To plot it, start at the origin and move 3 units to the left because the x-coordinate is negative. Then move 4 units downward because the y-coordinate is also negative. Mark the point at that position. Since both coordinates are negative, the point lies in the third quadrant. The third quadrant contains all points with negative x-values and negative y-values. Identifying the quadrant helps in understanding the relative position of points on the coordinate plane.
Q13. What are positive and negative coordinates?
Answer:
Positive and negative coordinates indicate the direction of a point from the origin. A positive x-coordinate means the point lies to the right of the y-axis, while a negative x-coordinate means it lies to the left. Similarly, a positive y-coordinate means the point lies above the x-axis, and a negative y-coordinate means it lies below the x-axis. The combination of positive and negative coordinates determines the quadrant in which the point lies. Understanding the signs of coordinates is essential for plotting points correctly and interpreting graphs accurately.
Q14. How can you identify the quadrant of a point without plotting it?
Answer:
A point’s quadrant can be identified by examining the signs of its coordinates. If both x and y are positive, the point lies in the first quadrant. If x is negative and y is positive, it lies in the second quadrant. If both coordinates are negative, it lies in the third quadrant. If x is positive and y is negative, it lies in the fourth quadrant. This method allows quick identification of a point’s location without drawing a graph. It is a useful skill for solving coordinate geometry questions efficiently.
Q15. What is meant by the abscissa and ordinate of a point?
Answer:
The abscissa of a point is its x-coordinate, while the ordinate is its y-coordinate. For example, in the point (4, −3), the abscissa is 4 and the ordinate is −3. The abscissa indicates the horizontal distance from the y-axis, whereas the ordinate indicates the vertical distance from the x-axis. These terms are commonly used in coordinate geometry to describe the position of a point. Understanding abscissa and ordinate helps students interpret coordinates correctly and communicate mathematical ideas more precisely.
Q16. Write the coordinates of points in all four quadrants.
Answer:
Each quadrant has a unique combination of coordinate signs. In the first quadrant, both coordinates are positive, such as (2, 3). In the second quadrant, the x-coordinate is negative and the y-coordinate is positive, such as (−2, 3). In the third quadrant, both coordinates are negative, such as (−2, −3). In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative, such as (2, −3). Knowing these sign patterns helps students identify quadrants quickly and plot points accurately on the coordinate plane.
Q17. Why is the origin important in coordinate geometry?
Answer:
The origin is the reference point of the coordinate plane where the x-axis and y-axis intersect. Its coordinates are (0, 0). All coordinates are measured relative to the origin. Positive and negative directions on both axes are determined from this point. The origin helps in locating points, measuring distances, and understanding geometric relationships. It is the starting point for plotting any coordinate on a graph. Without the origin, it would be impossible to define the positions of points accurately in coordinate geometry.
Q18. How does coordinate geometry connect algebra and geometry?
Answer:
Coordinate geometry combines algebra and geometry by representing geometric figures through numerical coordinates and equations. Points, lines, and shapes can be studied using algebraic methods. For example, the position of a point is described by an ordered pair, and geometric relationships can be expressed through equations. This approach makes calculations more systematic and accurate. Coordinate geometry helps solve problems involving distance, midpoint, and area using algebraic formulas. Thus, it acts as a bridge between algebra and geometry, making mathematical analysis more powerful and efficient.
Q19. What precautions should be taken while plotting points?
Answer:
While plotting points, students should first draw the axes clearly and mark equal units on both axes. The coordinates should be read carefully to avoid interchanging the x and y values. Positive and negative signs must be checked before plotting. Movement along the x-axis should be completed first, followed by movement parallel to the y-axis. Points should be marked neatly and labeled correctly. Following these precautions ensures accuracy in graphing and helps avoid errors in solving coordinate geometry problems. Proper plotting is essential for obtaining correct mathematical results.
Q20. Explain the importance of quadrants in coordinate geometry.
Answer:
Quadrants help divide the coordinate plane into four distinct regions, making it easier to identify the location of points. Each quadrant has a specific combination of positive and negative coordinate values. By observing the signs of the coordinates, one can determine the quadrant without plotting the point. Quadrants are useful in graphing, navigation, engineering, and data representation. They help describe positions accurately and simplify the study of geometric relationships. Understanding quadrants is one of the fundamental concepts of coordinate geometry and forms the basis for many advanced mathematical topics.