Complete Solutions and Summary of Coordinate Geometry – NCERT Class 9, Mathematics, Chapter 3 – Summary, Questions, Answers, Extra Questions
Detailed summary and explanation of Chapter 3 ‘Coordinate Geometry’ with all question answers, extra questions, and solutions from NCERT Class IX, Mathematics.
Updated: 7 months ago
Categories: NCERT, Class IX, Mathematics, Summary, Extra Questions, Coordinate Geometry, Chapter 3
Coordinate geometry uses x and y axes to locate points in a plane with ordered pairs (x,y). Quadrants divide the plane, signs determine location. Developed by René Descartes.
Comprehensive Chapter Summary
1. Introduction
Locating points on number line: One dimension.
Plane positions: Need two references, e.g., street and house number.
Examples: Friend's house on Street 2, House 5 as H; Street 7, House 4 as P.
Dot on paper: Distance from left (5cm) and bottom (9cm).
Seating plan: Column and row, e.g., (5,3) for 5th column, 3rd row.
Two independent infos: For plane positions.
Coordinate geometry: Branch using this idea.
René Descartes: Developer of system.
Basic concepts: Introduced here, more in higher classes.
Applications: Maps, graphs, positions in 2D.
Extension: To 3D with z-axis.
Historical: Latitude/longitude precursor.
Activity: Seating plan to understand coordinates.
Teacher as observer: Origin not part of seating.
Notation: (column, row).
Far-reaching: Basis for analytics, calculus.
Seating Plan
Draw seating, use (column, row) for positions.
2. Cartesian System
Number line: Distances from origin positive/negative.
Two lines: X'X horizontal, Y'Y vertical.
Cross at origins: Plane divided into quadrants I-IV anticlockwise.
Axes: x-axis horizontal, y-axis vertical.
Positive directions: OX right, OY up.
Coordinates: x from y-axis (abscissa), y from x-axis (ordinate).
Notation: (x,y), x first.
Quadrants: I(+,+), II(-,+), III(-,-), IV(+,-).
On axes: x-axis (x,0), y-axis (0,y).
Origin: (0,0).
Convention: Accepted worldwide.
Graph paper: For plotting.
Perpendicular distances: To axes.
Signs: Determine quadrant.
Examples: Points A(4,0), B(0,3), etc.
History: Descartes in bed, fly on ceiling inspiration.
Quadrants
I: +x +y, II: -x +y, III: -x -y, IV: +x -y.
Axes
x horizontal, y vertical.
Example: Coordinates
Point P(4,3), Q(-6,-2).
3. Plotting a Point in the Plane if its Coordinates are Given
Plot: From origin, move x along x-axis, y along y-axis.
Examples: Points in quadrants, on axes.
Graph paper: Units for accuracy.
Perpendiculars: To find distances.
Unique: Each point unique coordinates.
(x,y) ≠ (y,x) unless x=y.
Exercises: Fill coordinates from fig.
Applications: Graphs, maps.
Extension: Distance formula, midpoint later.
Visualize: Points in plane.
Negative: Left/down.
Positive: Right/up.
Origin: No movement.
Street plan: Scale 1cm=200m, cross-streets (2,5).
One (4,3): Unique intersection.
(3,4) different from (4,3).
Key Concepts and Definitions
Cartesian Plane
xy-plane with axes.
Abscissa
x-coordinate.
Ordinate
y-coordinate.
Origin
(0,0).
Quadrant
Four regions.
x-axis
Horizontal line.
y-axis
Vertical line.
Important Facts
I(+,+)
II(-,+)
III(-,-)
IV(+,-)
Origin(0,0)
Questions and Answers from Chapter
Short Questions (1 Mark)
Q1. What is the name of horizontal and vertical lines in Cartesian plane?
Answer: x-axis, y-axis.
Q2. What is the name of each part of the plane formed by axes?
Answer: Quadrant.
Q3. What is the point of intersection of axes?
Answer: Origin.
Q5. What are coordinates of origin?
Answer: (0,0).
Q6. What is abscissa?
Answer: x-coordinate.
Q7. What is ordinate?
Answer: y-coordinate.
Q8. Signs in first quadrant?
Answer: (+,+).
Q9. Signs in second quadrant?
Answer: (-,+).
Q10. Signs in third quadrant?
Answer: (-,-).
Q11. Signs in fourth quadrant?
Answer: (+,-).
Q12. Coordinates on x-axis?
Answer: (x,0).
Q13. Coordinates on y-axis?
Answer: (0,y).
Q14. Who developed Cartesian system?
Answer: René Descartes.
Q15. What is Cartesian plane?
Answer: xy-plane.
Q16. Number of quadrants?
Answer: 4.
Q17. Positive x-direction?
Answer: Right.
Q18. Positive y-direction?
Answer: Up.
Q19. (3,4) quadrant?
Answer: I.
Q20. (-3,4) quadrant?
Answer: II.
Medium Questions (3 Marks)
Q1. Describe position of table lamp on study table.
Answer: Use distances from two edges, e.g., 30cm from left, 40cm from bottom.
Q2. In street plan, how many cross-streets (4,3)?
Answer: One unique intersection.
Q3. In street plan, how many cross-streets (3,4)?
Answer: One, but different from (4,3).
Q4. Write name of horizontal and vertical lines.
Answer: x-axis, y-axis.
Q5. Name parts formed by axes.
Answer: Quadrants.
Q6. Name intersection point.
Answer: Origin.
Q7. Coordinates of B from fig.
Answer: (-5,2).
Q8. Coordinates of C from fig.
Answer: (5,-5).
Q9. Point for coordinates (-3,-5).
Answer: G.
Q10. Point for (2,-4).
Answer: H.
Q11. Abscissa of D.
Answer: -3.
Q12. Ordinate of H.
Answer: 5.
Q13. Coordinates of L.
Answer: (0,5).
Q14. Coordinates of M.
Answer: (3,0).
Q15. What is x-coordinate?
Answer: Distance from y-axis.
Q16. What is y-coordinate?
Answer: Distance from x-axis.
Q17. Signs in III quadrant.
Answer: (-,-).
Q18. Point on x-axis form.
Answer: (x,0).
Q19. Point on y-axis form.
Answer: (0,y).
Q20. Is (3,4) same as (4,3)?
Answer: No.
Long Questions (6 Marks)
Q1. How to describe position of table lamp on study table.
Answer: Measure distance from two perpendicular edges, say left and front. E.g., 30cm from left, 40cm from front. Like coordinates.
Q2. In city with two main roads crossing at centre, roads N-S and E-W, 5 streets each direction 200m apart. Draw model 1cm=200m. How many cross-streets (4,3)?
Answer: One unique. Draw grid, label.
Q3. How many cross-streets (3,4)?
Answer: One, different from (4,3).
Q4. Name horizontal and vertical lines for position.
Answer: x-axis horizontal, y-axis vertical.
Q5. Name parts formed by lines.
Answer: Quadrants I,II,III,IV.
Q6. Name intersection point.
Answer: Origin.
Q7. Coordinates of B from fig 3.14.
Answer: (-2,4).
Q8. Coordinates of C from fig.
Answer: (5, -5).
Q9. Point for (-3,-5).
Answer: E.
Q10. Point for (2,-4).
Answer: G.
Q11. Abscissa of D.
Answer: 3.
Q12. Ordinate of H.
Answer: 5.
Q13. Coordinates of L.
Answer: (0,5).
Q14. Coordinates of M.
Answer: (-3,0).
Q15. Explain Cartesian system.
Answer: Two perpendicular axes, x horizontal, y vertical, intersect at origin. Points (x,y).
Q16. How to plot (4,3).
Answer: 4 right from origin, 3 up.
Q17. Signs in quadrants.
Answer: I(+,+), II(-,+), III(-,-), IV(+,-).
Q18. What is coordinate geometry?
Answer: Describing positions in plane using numbers.
