CBSE Class 9 Maths Notes Coordinate Geometry

Q: What is Coordinate Geometry in CBSE Class 9 Maths and why is it important?

Coordinate Geometry is an important chapter in CBSE Class 9 Maths that introduces students to the Cartesian plane and the method of locating points using coordinates. This chapter explains concepts such as coordinate geometry, Cartesian coordinate system, x-axis, y-axis, origin, ordered pair, and plotting points on a graph. Students often search for coordinate geometry notes, Cartesian plane explanation, coordinate graph examples, and Class 9 Maths important questions because these topics frequently appear in exams. Coordinate Geometry helps connect algebra and geometry by representing geometric figures through numerical values. Understanding how to identify and locate points on a graph improves analytical and visualization skills. A strong grasp of this chapter forms the foundation for advanced mathematical topics such as distance formula, midpoint formula, and graphing in higher classes.

Q: What are the Cartesian Plane, Axes, and Quadrants in Coordinate Geometry?

The Cartesian Plane is a two-dimensional graph formed by two perpendicular number lines known as the x-axis and y-axis. Their intersection point is called the origin, represented by (0,0). One of the most searched topics in Coordinate Geometry is understanding quadrants and coordinates. The Cartesian Plane is divided into four quadrants where points are located based on positive and negative values of x and y coordinates. Students should learn how ordered pairs are written and how points are plotted accurately on a graph. Keywords such as quadrants in coordinate geometry, coordinate axes, origin in maths, plotting points, and graph representation are highly important for examinations. Regular practice with graph-based questions helps students develop accuracy and confidence while solving coordinate geometry problems in Class 9 Maths.

Q: How can students score high marks in the Class 9 Coordinate Geometry chapter?

To score well in Coordinate Geometry, students should focus on understanding the Cartesian coordinate system rather than memorizing definitions. Begin by learning the concepts of x-axis, y-axis, origin, quadrants, coordinates, and ordered pairs. Practice plotting points on graph paper and identifying the coordinates of given points. Students frequently search for coordinate geometry formulas, NCERT solutions, important questions, revision notes, and exam preparation tips. Although this chapter contains fewer formulas than later geometry chapters, conceptual clarity is essential. Solving all NCERT exercises, sample questions, and diagram-based problems can improve performance significantly. Creating short revision notes for key definitions and practicing graph questions regularly helps strengthen understanding. Consistent revision and careful observation of coordinates can help students achieve excellent marks in examinations.

Coordinate SystemQuadrantsPlotting PointsDistance FormulaLinear GraphsKey PointsExercise 1Exercise 2

Theory

Co-ordinate System

📐Two Types of Co-ordinate Systems

In two-dimensional coordinate geometry, we generally use two types of co-ordinate systems:

(i) Cartesian or Rectangular Co-ordinate System — A point is represented by an ordered pair (x, y), where x is the x-coordinate and y is the y-coordinate.
(ii) Polar Co-ordinate System — A point is represented by an ordered pair (r, θ), where r is the radius vector (distance from origin) and θ (theta) is the vectorial angle measured from the positive x-axis.

Ordered Pair

Definition: A pair of real numbers p and q listed in a specific order — with p at the first place and q at the second — is called an ordered pair, written as (p, q). This is also known as the coordinates of a point in space.

⚠️ Note: (p, q) and (q, p) represent two different points unless p = q.

Coordinate Axes

Draw two straight lines XOX′ and YOY′ intersecting at right angles at point O. These lines are called coordinate axes or axes of reference.

Y (positive) ↑ | II | I (−, +) | (+, +) | ────────────────────O──────────────────→ X (positive) | III | IV (−, −) | (+, −) | Y′ (negative) OX → Positive x-axis OX′ → Negative x-axis OY → Positive y-axis OY′ → Negative y-axis O = Origin (0, 0)

📌Key Terminology

The horizontal line XOX′ is the x-axis.
The vertical line YOY′ is the y-axis.
The point O where both axes meet is called the origin. Its coordinates are (0, 0).
The distance measured along the x-axis is called the x-coordinate or abscissa.
The distance measured along the y-axis is called the y-coordinate or ordinate.
A point P(x, y): x is written first, y is written second.

Theory

Quadrants & Convention of Signs

The two coordinate axes XOX′ and YOY′ divide the plane into four regions called quadrants:

Quadrant I (XOY)x > 0 , y > 0 → (+, +)
Both coordinates positive

Quadrant II (YOX′)x < 0 , y > 0 → (−, +)
x negative, y positive

Quadrant III (X′OY′)x < 0 , y < 0 → (−, −)
Both coordinates negative

Quadrant IV (Y′OX)x > 0 , y < 0 → (+, −)
x positive, y negative

Points on the Axes

On the x-axis: The y-coordinate is zero. Points are of the form (x, 0).
On the y-axis: The x-coordinate is zero. Points are of the form (0, y).
At the origin: Both coordinates are zero → (0, 0).

📝 Example 1 — Identifying Quadrants

Q. In which quadrant do the given points lie?
(i) A(3, 4) (ii) B(−2, 3) (iii) C(−5, −2) (iv) D(4, −3) (v) E(−5, −5)

SOLUTION

Point	Signs (x, y)	Quadrant
A(3, 4)	(+, +)	I
B(−2, 3)	(−, +)	II
C(−5, −2)	(−, −)	III
D(4, −3)	(+, −)	IV
E(−5, −5)	(−, −)	III

📝 Example 2 — Points on Axes

Q. Which of the following points lie on the x-axis or y-axis?
(−3, 4), (0, 8), (2, −3), (−6, 0)

SOLUTION

(0, 8) → x-coordinate = 0 → lies on the y-axis.

(−6, 0) → y-coordinate = 0 → lies on the x-axis.

(−3, 4) and (2, −3) lie in Quadrant II and Quadrant IV respectively — neither axis.

Theory

Plotting of Points

To plot a point P(a, b) in the Cartesian plane, follow this algorithm:

Draw two mutually perpendicular lines on graph paper — one horizontal (x-axis) and one vertical (y-axis).

Mark their intersection point as O (the origin).

Choose a suitable scale on both axes and mark equal unit distances.

Start from origin. Move |a| units along OX (if a > 0) or OX′ (if a < 0). Call this point M.

From M, move |b| units vertically upward (if b > 0) or downward (if b < 0). This final position is P(a, b).

📝 Example 3 — Plotting a Point

Q. Plot the point (3, 4) on a graph paper.

SOLUTION

Let X′OX and Y′OY be the coordinate axes. For P(3, 4):

Y 5 · 4 · P(3,4) ● 3 · 2 · 1 · 0 ·─────────────────────── X 0 1 2 3 4 Step 1: Move 3 units right along OX → reach M(3, 0) Step 2: From M, move 4 units upward → reach P(3, 4) ✓

📝 Example 4 — Plotting Multiple Points

Q. Plot the following points: A(2, 5), B(−5, −7), C(3, −2), D(0, 5), E(5, 0).

SOLUTION

Y 5 D(0,5) ● A(2,5) ● 4 3 2 1 0 ──────────────────────────── X -1 C(3,−2) ● -2 -5 B(−5,−7) ● E(5, 0) lies on the x-axis (y = 0) D(0, 5) lies on the y-axis (x = 0) B(−5,−7) is in Quadrant III C(3,−2) is in Quadrant IV A(2, 5) is in Quadrant I

Formula

Distance Between Two Points

📏Distance Formula

If there are two points A(x₁, y₁) and B(x₂, y₂) on the XY plane, the distance d between them is:

AB = d = √[ (x₂ − x₁)² + (y₂ − y₁)² ]

This is derived from the Pythagorean theorem: the horizontal and vertical separations form the two legs of a right triangle, and AB is the hypotenuse.

💡 Special Cases:
• Distance from origin to point P(x, y): OP = √(x² + y²)
• If two points lie on the x-axis (y = 0): distance = |x₂ − x₁|
• If two points lie on the y-axis (x = 0): distance = |y₂ − y₁|

📝 Example 5 — Distance Calculations

Q. Find the distance between:

(i) (5, 3) and (3, 2) (ii) (−1, 4) and (2, −3) (iii) (a, b) and (−b, a)

SOLUTION

(i) d₁ = √[(3 − 5)² + (2 − 3)²]

= √[(−2)² + (−1)²] = √[4 + 1] = √5 units

(ii) d₂ = √[(2 − (−1))² + (−3 − 4)²]

= √[(3)² + (−7)²] = √[9 + 49] = √58 units

(iii) d₃ = √[(−b − a)² + (a − b)²]

= √[(a + b)² + (a − b)²] = √[a² + 2ab + b² + a² − 2ab + b²] = √[2a² + 2b²] = √[2(a² + b²)] units

Theory

Graph of Linear Equation ax + by + c = 0

📈Slope-Intercept Form

The general linear equation ax + by + c = 0 can be rewritten as:

y = mx + c

where:

m = −a/b is called the slope (or gradient) of the line.
c = −c₁/b is called the y-intercept (where the line cuts the y-axis).

Steps to Draw the Graph

Rearrange the equation to find y in terms of x: form y = mx + c.

Assume three integer values of x and calculate corresponding y values.

Prepare a table of ordered pairs (x, y).

Plot these points on a graph paper using a suitable scale.

Join the plotted points in a straight line — this is the graph of ax + by + c = 0.

📝 Example 6 — Drawing the Graph of y = mx + c

Q. Draw the graph of the line y = mx + c.

SOLUTION

Prepare a table of values. For x = 0, y = c. For y = 0, x = −c/m. For x = −c/m, we get x = −c/m.

x	0	−c/m	−2c/m
y	c	0	−c

Y | / | / ← slope = m | / |/______ (x-intercept at −c/m, 0) O──────────────── X | intercept on y-axis = c (point A = OA)

Key Observations:
1. The graph changes if the signs of m and c differ.
2. m (coefficient of x) is the slope of the line.
3. c is the y-intercept (where the line crosses the y-axis), i.e., OA = c.

Special Linear Graphs

y = c (constant)A horizontal lineparallel to the x-axisat height c.
Slope = 0

x = c (constant)A vertical lineparallel to the y-axisat distance c.
Slope = undefined

y = mx (c = 0)Passes through theorigin (0, 0).
y-intercept = 0

y = x (m = 1, c = 0)Equally inclined to both axes (45°).
Passes through origin

🔄Effect of Slope m on y = mx

Value of m	Position / Rotation	Quadrants
m > 0 (positive, increasing)	Line rotates anticlockwise as m increases	I and III
m < 0 (negative, decreasing)	Line rotates clockwise as \|m\| increases	II and IV
m = 0	Horizontal line (y = 0, the x-axis)	—

↕️Effect of Y-Intercept c on y = mx + c

Changing c to c₁, c₂, c₃ … gives parallel lines (same slope, different y-intercepts).
Increasing c shifts the graph upward.
Decreasing c shifts the graph downward.

📝 Example 7 — Effect of Signs of m and c on y = mx + c

SOLUTION

The positioning of the graph depends on the sign combination of m and c:

m	c	Graph Description
+	+	Rises left to right; crosses y-axis above origin
+	−	Rises left to right; crosses y-axis below origin
−	+	Falls left to right; crosses y-axis above origin
−	−	Falls left to right; crosses y-axis below origin

📝 Example 8 — Draw graph of y = 3x + 6

Q. Draw the graph of y = 3x + 6. Find (i) slope (ii) y-intercept (iii) area between the line and axes.

SOLUTION

Comparing with y = mx + c: m = 3, c = 6.

x	0	−2	−1
y	6	0	3

The line cuts the y-axis at (0, 6) and the x-axis at (−2, 0).

Y 6 ● ← y-intercept (0, 6) 5 4 3 2 1 0 ──────────────────── X -3 -2 -1 ● ← x-intercept (−2, 0) Area between line and axes = ½ × base × height = ½ × 2 × 6 = 6 square units

(i) Slope = 3 | (ii) y-intercept = 6 units (OA = 6) | (iii) Area = 6 square units

Summary

Key Points to Remember

Two perpendicular lines XOX′ and YOY′ intersecting at O are thecoordinate axes.
Origin O has coordinates(0, 0). The abscissa of every point on the y-axis is zero; the ordinate of every point on the x-axis is zero.
The four quadrants have signs: I → (+,+), II → (−,+), III → (−,−), IV → (+,−).
Theabscissa (x)is the perpendicular distance from the y-axis. Theordinate (y)is the perpendicular distance from the x-axis.
Distance formula:AB = √[(x₂−x₁)² + (y₂−y₁)²]
Iny = mx + c: m is the slope; c is the y-intercept.
y = c→ parallel to x-axis; x = c→ parallel to y-axis.
For y = mx with m > 0: graph is in Quadrants I & III and rotates anticlockwise as m increases.
For y = mx with m < 0: graph is in Quadrants II & IV and rotates clockwise as |m| increases.
Changing c shifts parallel lines: increasing c moves graph up; decreasing c moves graph down.

Practice

Let's Try — Quick Practice

#	Question
1	In which quadrant do the given points lie? (i) (3, −5) (ii) (−4, 6) (iii) (−3, −1) (iv) (2, 5)
2	Which of the given points lie on the x or y axis? (−3, 4), (0, 8), (2, −3), (−6, 0)
3	Plot the points O(0,0), A(16,0), B(16,12) on graph paper. Join OB, OA and BA. Name the figure and find its area.
4	Draw the graph of y = 3x + 6. Find (i) slope (ii) intercept on y-axis (iii) area between the line and axes.

Answers:
1. (i) IV quadrant (ii) II quadrant (iii) III quadrant (iv) I quadrant
2. (0, 8) → y-axis; (−6, 0) → x-axis
3. Right triangle; Area = ½ × 16 × 12 = 96 square units
4. Slope = 3; y-intercept OA = 6 units; Area = 6 square units

Exercise 1

MCQ Exercise – 1

1. Which point lies on the x-axis?
(a) (3, 2)
(b) (−3, 2)
(c) (2, 0) ✓
(d) (1, 2)
2. Which point lies on the y-axis?
(a) (1, 3)
(b) (0, 3) ✓
(c) (5, 2)
(d) (2, 3)
3. Which point lies above the x-axis?
(a) (1, 2) ✓
(b) (2, 0)
(c) (1, −5)
(d) (0, −3)
4. Which point lies to the left of the y-axis?
(a) (2, 0)
(b) (−3, 4) ✓
(c) (4, 2)
(d) (2, 7)
5. Which point lies to the right of the y-axis?
(a) (0, 3)
(b) (−2, 1)
(c) (2, −5) ✓
(d) (−3, 2)
6. Which line is parallel to y = x − 2?
(a) y = 2x + 1
(b) 2y = 2x − 6 ✓
(c) 2y = x + 7
(d) y = 3x + 1
Reason: 2y = 2x − 6 simplifies to y = x − 3, which has slope 1 — same as y = x − 2. Parallel lines have equal slopes.
7. Which point lies in the IV quadrant?
(a) (2, 3)
(b) (1, −4) ✓
(c) (−2, 3)
(d) (0, 1)
8. Which point lies in the III quadrant?
(a) (0, −3)
(b) (2, 0)
(c) (7, −2)
(d) (−2, −3) ✓
9. Which graph is parallel to the x-axis?
(a) y = x + 1
(b) y = 2 ✓
(c) x = 3
(d) x = 2y
10. Which graph is equally inclined to both axes?
(a) y = 2
(b) x = 2y
(c) 2y = x
(d) 2y = 2x ✓ (i.e., y = x)
11. The abscissa of a point is the distance of the point from:
(a) X-axis
(b) Y-axis ✓
(c) Origin
(d) None of these
12. The y-coordinate of a point is the distance of that point from:
(a) X-axis ✓
(b) Y-axis
(c) Origin
(d) None of these
13. If both coordinates of any point are negative, then that point will lie in:
(a) First quadrant
(b) Second quadrant
(c) Third quadrant ✓
(d) Fourth quadrant
14. If the abscissa of any point is zero, then that point will lie:
(a) on X-axis
(b) on Y-axis ✓
(c) at origin
(d) None of these
15. One end of a diameter of a circle is (4, −1) and the centre is (1, −3). The coordinates of the other end are:
(a) (2, 5)
(b) (−2, −5) ✓
(c) (3, 2)
(d) (−3, −2)
Using mid-point formula: Centre = midpoint → (1, −3) = ((4+x)/2, (−1+y)/2) → x = −2, y = −5.
16. The points (−2,−1), (1,0), (4,3) and (1,2) are the vertices of a:
(a) Rectangle
(b) Parallelogram ✓
(c) Square
(d) Rhombus
17. The distance of the point (3, 5) from the x-axis is:
(a) √34
(b) 3
(c) 5 ✓
(d) None of these
The distance from the x-axis is simply the ordinate (y-coordinate) = 5.

Answers to Exercise 1:
1.(c) · 2.(b) · 3.(a) · 4.(b) · 5.(c) · 6.(b) · 7.(b) · 8.(d) · 9.(b) · 10.(d) · 11.(b) · 12.(a) · 13.(c) · 14.(b) · 15.(b) · 16.(b) · 17.(c)

Exercise 2

Descriptive Exercise – 2

Question

Plot the points in the plane if coordinates are: A(5,0), B(0,3), C(7,2), D(−4,3), E(−3,−2) and F(3,−2).

In which quadrant do the following points lie? A(2,3), B(−2,3), C(−3,−5), D(3,−1). Explain with reasons.

Plot the following pairs of numbers as points in the Cartesian plane:

x	−3	−2	8	4	0
y	5	0	3	8	−2

With rectangular axes, plot O(0,0), A(4,0) and C(0,6). Find the coordinates of the fourth point B such that OABC forms a rectangle.

Plot P(−3,1) and Q(2,1) in the rectangular coordinate system. Find all possible coordinates of the other two vertices of a square having P and Q as two adjacent vertices.

Find the value of x if the distance between (x, −1) and (3, 2) is 5.

The base AB of two equilateral triangles ABC and ABC′ with side 2a lies along the x-axis such that the midpoint of AB is at the origin. Find the coordinates of C and C′.

Name the quadrants in which the following points lie: (a) (2, 3) (b) (3, −2).

Determine the slope and y-intercept of the graph of y = (1/2)x − 2.

Draw the graph of the equation y = 2x + 3.

Draw the graph of y = 4x. From the graph find the value of y when x = 2.

Draw the graph of 3x + 6y = 12. Find the coordinates of the point where the graph cuts the y-axis.

Draw the graph of x + 10 = 0. What type of graph is it?

The points (2, 5) and (3, 5) are plotted in xy plane. Find the slope and y-intercept of the line joining the points. [Hint: both points have same y-coordinate]

Draw the graphs of (i) y = x, (ii) y = x + 1, (iii) y = x + 2 on the same axes.

Draw the graphs of (i) y = 2x, (ii) y = 2x + 1, (iii) y = 2x + 3 on the same axes.

Draw the graphs of (i) y = 2x, (ii) y = 3x, (iii) y = 4x on the same axes.

Selected Answers to Exercise 2:
2. A → I, B → II, C → III, D → IV
4. B = (4, 6)
5. Other vertices: (−3, 6) & (2, 6) or (−3, −4) & (2, −4)
6. x = 7 or x = −1
7. C = (0, a√3), C′ = (0, −a√3)
8. (a) Quadrant I (b) Quadrant IV
9. Slope = 1/2, y-intercept = −2
11. When x = 2, y = 8 (from y = 4x)
15. Graph cuts y-axis at (0, 2)
16. x = −10 is a vertical line parallel to the y-axis
17. Slope = 0 (horizontal line), y-intercept = 5

Notes

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FAQs on CBSE Class 9 Maths Notes Coordinate Geometry – Concepts & FAQs

What is Coordinate Geometry in CBSE Class 9 Maths and why is it important?+

What are the Cartesian Plane, Axes, and Quadrants in Coordinate Geometry?+

How can students score high marks in the Class 9 Coordinate Geometry chapter?+

Coordinate Geometry

Co-ordinate System

Ordered Pair

Coordinate Axes

Quadrants & Convention of Signs

Points on the Axes

Plotting of Points

Distance Between Two Points

Graph of Linear Equation ax + by + c = 0

Steps to Draw the Graph

Special Linear Graphs

Key Points to Remember

Let's Try — Quick Practice

MCQ Exercise – 1

Descriptive Exercise – 2

Make Your Own Notes

FAQs on CBSE Class 9 Maths Notes Coordinate Geometry – Concepts & FAQs

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Coordinate Geometry

Co-ordinate System

Ordered Pair

Coordinate Axes

Quadrants & Convention of Signs

Points on the Axes

Plotting of Points

Distance Between Two Points

Graph of Linear Equation ax + by + c = 0

Steps to Draw the Graph

Special Linear Graphs

Key Points to Remember

Let's Try — Quick Practice

MCQ Exercise – 1

Descriptive Exercise – 2

Make Your Own Notes

FAQs on CBSE Class 9 Maths Notes Coordinate Geometry – Concepts & FAQs

MYSY Scholarship 2026 - Eligibility, Last Date, Amount, Apply Online & Benefits

Vidyadhan Scholarship 2026 - Apply Online, Eligibility, Last Date, Amount & Complete Details

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Introduction to Euclid's Geometry

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