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Rajasthan (RBSE)Class 9 Mathematics★ 4–6 marks · RBSE Class 9 Mathematics (new NCF — Ganita Prakash 9)

The Use of Coordinates — The Cartesian System

The new NCF Class 9 Maths chapter that opens the year — locating a point with coordinates. The two perpendicular axes, the origin, ordered pairs (x, y), abscissa and ordinate, the four quadrants and their sign rules, and plotting points on the Cartesian plane — with solved board-pattern problems.

⏱ 26 min readEasy difficulty✓ Free · NCERT-aligned

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The chapter at a glance

Every concept and exam-favourite branch — revisable in 5 minutes.

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Study Guide

Night-before notes

Key points, glossary and the questions most likely to show up.

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By the end of this chapter you'll be able to…

1Explain why a point on a plane needs two coordinates
2Identify the x-axis, y-axis, origin, abscissa and ordinate
3State the sign pattern of each of the four quadrants
4Plot a point from its ordered pair and read a point off a graph
5Recognise points lying on the axes (x = 0 or y = 0)

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Why this chapter matters

Coordinates link algebra and geometry and are the basis for graphs, lines and Class 10 Coordinate Geometry (distance and section formulae). The question types — name the quadrant, plot a point, read coordinates — are quick, predictable marks if you are careful with signs.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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The World of Numbers (Class 9)

Positive and negative numbers on the number line.

The Use of Coordinates — The Cartesian System (RBSE Class 9 · Mathematics)

"Where exactly is it?" A single number can place you on a line, but to pin a point on a flat surface you need two. That pair of numbers — coordinates — is one of the most powerful ideas in mathematics, linking algebra and geometry.

RBSE note (2026-27). Class 9 uses the new NCF (Ganita Prakash 9) Mathematics textbook. Orienting Yourself: The Use of Coordinates is the opening chapter. BSER (Ajmer) sets the exam.

1. From one number to two

On a number line a single number fixes a position. But a point on a plane (like a seat in a hall — row and column) needs two numbers. René Descartes' idea: use two perpendicular number lines.

2. The Cartesian coordinate system

The horizontal line is the x-axis; the vertical line is the y-axis.
They meet at the origin O, with coordinates (0, 0).
A point P is written as an ordered pair (x, y):
- x-coordinate (abscissa): distance from the y-axis (right +, left −).
- y-coordinate (ordinate): distance from the x-axis (up +, down −).

Order matters: (x, y) is an ordered pair. In general (x, y) ≠ (y, x); they are equal only when x = y.

3. The four quadrants

The axes divide the plane into four quadrants, numbered anticlockwise:

Quadrant	x sign	y sign	Example
I	+	+	(3, 2)
II	−	+	(−3, 2)
III	−	−	(−3, −2)
IV	+	−	(3, −2)

Special cases:

A point on the x-axis has y = 0, i.e. (x, 0).
A point on the y-axis has x = 0, i.e. (0, y).
The origin is (0, 0).

4. Plotting a point

To plot (x, y): start at the origin, move x units along the x-axis (right if +, left if −), then y units parallel to the y-axis (up if +, down if −), and mark the point. Reading a point off a graph reverses this: read its horizontal then vertical distance.

5. Worked example

In which quadrant or on which axis do these lie: A(4, 0), B(−2, 5), C(−3, −1), D(0, −4.5)?

A(4, 0): y = 0 → on the x-axis.
B(−2, 5): x −, y + → Quadrant II.
C(−3, −1): both − → Quadrant III.
D(0, −4.5): x = 0 → on the y-axis (below the origin).

6. Quick recap

A point on a plane needs two numbers — an ordered pair (x, y).
x-axis (horizontal), y-axis (vertical), meeting at the origin (0, 0).
Abscissa = x (from y-axis); ordinate = y (from x-axis); (x, y) ≠ (y, x) in general.
Quadrants I–IV (anticlockwise) have sign patterns (+,+), (−,+), (−,−), (+,−).
On the x-axis y = 0; on the y-axis x = 0.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Ordered pair

P = (x, y)

x = abscissa (from y-axis), y = ordinate (from x-axis).

Origin

O = (0, 0)

Where the axes meet.

On x-axis

(x, 0)

y-coordinate is 0.

On y-axis

(0, y)

x-coordinate is 0.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Writing the coordinates in the wrong order

✓ It is ALWAYS (x, y): horizontal first, then vertical. (x, y) ≠ (y, x) unless x = y.

WATCH OUT

✗ Getting quadrant signs wrong

✓ Go anticlockwise from top-right: I (+,+), II (−,+), III (−,−), IV (+,−).

WATCH OUT

✗ Confusing abscissa and ordinate

✓ Abscissa = x (distance from the y-axis); ordinate = y (distance from the x-axis).

WATCH OUT

✗ Plotting (0, y) on the x-axis

✓ x = 0 means the point is on the y-AXIS; y = 0 means it is on the x-axis.

WATCH OUT

✗ Moving up for a negative y

✓ Negative y means DOWN; negative x means LEFT. Match sign to direction.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

In-text (axes & ordered pairs)

Abscissa/ordinate; (x,y) vs (y,x)

Questions

In-text (quadrants)

Identify quadrant from signs; points on axes

Questions

Activity — plotting

Plot given points; map a real room with coordinates

Questions

End-of-chapter Ex

End-of-chapter exercise

Plot, read and classify points

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Quadrant

In which quadrant does (−5, 3) lie?

▶ Show solution

x is negative, y is positive → Quadrant II.

✦ Answer: Quadrant II.

Q2EASY· Axis

Where does the point (0, 7) lie?

▶ Show solution

x = 0, so it lies on the y-axis (7 units above the origin).

✦ Answer: on the y-axis.

Q3EASY· Terminology

What is the abscissa of the point (−4, 9)?

▶ Show solution

The abscissa is the x-coordinate.

✦ Answer: −4.

Q4MEDIUM· Order

Are the points (2, 3) and (3, 2) the same? Justify.

▶ Show solution

Step 1 — Coordinates are an ordered pair (x, y).

Step 2 — (2, 3) has x = 2, y = 3; (3, 2) has x = 3, y = 2 — different positions.

✦ Answer: No; (x, y) ≠ (y, x) when x ≠ y.

Q5MEDIUM· Classify

Classify A(−3, −7) and B(6, 0) by quadrant or axis.

▶ Show solution

A(−3, −7): both negative → Quadrant III.

B(6, 0): y = 0 → on the x-axis.

✦ Answer: A — Quadrant III; B — x-axis.

Q6MEDIUM· Plot

State the coordinates of a point 5 units to the left of the origin and 2 units up.

▶ Show solution

Step 1 — left → x = −5; up → y = +2.

Step 2 — point is (−5, 2).

✦ Answer: (−5, 2) (Quadrant II).

Q7HARD· Reasoning

A point lies on the x-axis at distance 4 from the origin on the negative side. Another lies on the y-axis 3 units below the origin. Write both coordinates and name where each lies.

▶ Show solution

Step 1 — On the x-axis, y = 0; negative side at distance 4 → (−4, 0).

Step 2 — On the y-axis, x = 0; 3 units below → (0, −3).

✦ Answer: (−4, 0) on the x-axis; (0, −3) on the y-axis.

Q8HARD· Geometry

Plot P(2, 3), Q(2, −3) and R(−2, 3). What kind of figure do P, Q, R and S(−2, −3) form?

▶ Show solution

Step 1 — P(2,3) and Q(2,−3) share x = 2; R(−2,3) and S(−2,−3) share x = −2.

Step 2 — Horizontal sides length 4, vertical sides length 6, all angles 90°.

✦ Answer: a rectangle (4 × 6).

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•A plane point needs two numbers — the ordered pair (x, y).
•x-axis (horizontal), y-axis (vertical), origin (0, 0).
•Abscissa = x (from y-axis); ordinate = y (from x-axis); (x, y) ≠ (y, x) in general.
•Quadrants anticlockwise: I (+,+), II (−,+), III (−,−), IV (+,−).
•On the x-axis y = 0 → (x, 0); on the y-axis x = 0 → (0, y).
•Plot: move x along x-axis, then y parallel to y-axis (sign = direction).

Rajasthan (RBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 4–6 marks

Question type	Marks each	Typical count	What it tests
MCQ / fill in the blank	1	1–2	Quadrant from signs, point on axis, abscissa/ordinate
Short answer	2	1–2	Order of coordinates; classify points
Short answer + plotting	3	1	Plot points; identify the figure formed

Prep strategy

Memorise the quadrant sign wheel (anticlockwise from +,+)
Always write (x, y) — horizontal first
Practise plotting and reading points on graph paper
Remember: x = 0 → y-axis; y = 0 → x-axis

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Maps & GPS

Latitude and longitude are coordinates pinning any point on Earth.

Screens & pixels

Every pixel on your phone has (x, y) coordinates the device addresses.

Seating & spreadsheets

Row–column references (like B7) are everyday coordinate systems.

Robotics & CNC

Machines move tools to (x, y) targets on a plane.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Read/write coordinates as (x, y) — horizontal first, every time.
Use the quadrant sign wheel to classify points instantly.
For plotting, mark axes and scale first, then locate each point carefully.
Check axis cases (x = 0 or y = 0) before assigning a quadrant.
On figure questions, compare shared x- or y-coordinates to spot rectangles/squares.

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Distance between two points and the midpoint formula (Class 10 preview).
Reflections of a point across the axes and the origin.
Coordinates in 3-D: adding a z-axis.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

RBSE Class 9 Annual (BSER Ajmer)Medium-high — plotting + quadrant questions

NTSE / NMMSMedium — coordinate MCQs

JEE FoundationHigh — base for Class 10 Coordinate Geometry

Maths Olympiad (IMO)Low-medium — coordinate methods in geometry

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Yes. Class 9 (2026-27) uses the new NCF NCERT 'Ganita Prakash 9' book; 'Orienting Yourself: The Use of Coordinates' introduces the Cartesian plane. BSER Ajmer sets the RBSE paper.

Because (x, y) is an ordered pair: the first number is the horizontal position and the second the vertical. Swapping them usually moves you to a different point.

Right is positive x and left is negative x; up is positive y and down is negative y.

(0, 0) — it lies on both axes, where they intersect.

Practice more, ask doubts, find a tutor

Rajasthan (RBSE) Class 9 mock tests

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