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.
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Categories: NCERT, Class IX, Mathematics, Summary, Extra Questions, Coordinate Geometry, Chapter 3
Tags: Coordinate Geometry, Cartesian Plane, Coordinates, Quadrants, Abscissa, Ordinate, Origin, x-axis, y-axis, Position, Graphs, NCERT, Mathematics, Class 9, Chapter 3, Answers, Extra Questions
Coordinate Geometry
Chapter 3: Mathematics - Complete Study Guide
Chapter Overview
X-Axis
Horizontal
Y-Axis
Vertical
Origin
(0,0)
Quadrants
Four Parts
What You'll Learn
Cartesian Plane
Two perpendicular axes to locate points.
Coordinates
Ordered pairs (x,y) for positions.
Plotting Points
How to graph points in quadrants.
Applications
Seating plans, maps, positions.
Key Highlights
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.
Q19. Who is René Descartes?
Answer: French mathematician, developed system.
Q20. Difference between (3,4) and (4,3).
Answer: Different points.
Interactive Knowledge Quiz
Test your understanding of Coordinate Geometry
Quick Revision Notes
Axes
- x horizontal
- y vertical
Quadrants
- I (+,+)
- II (-,+)
- III (-,-)
- IV (+,-)
Coordinates
- (x,y)
- Origin (0,0)
Exam Strategy Tips
- Plot points
- Identify quadrants
- Describe positions
- Use examples
- Draw diagrams
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