NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 1 Orienting Yourself The Use of Coordinates
Chapter 1 of the new Class 9 Maths book is called Orienting Yourself: The Use of Coordinates. It is the opening chapter of Ganita Manjari Part I, the NCERT book for session 2026-27.
This chapter teaches you how to describe the exact position of a point using two numbers. You learn the Cartesian plane, how to plot and read points, how to find the distance between two points, and how to find the midpoint of a line segment.
On this page you get the topic list, the formulas, solved examples and free step-by-step solutions for both Exercise Sets and the End of Chapter Exercises.
Chapter 1 at a Glance
| Detail | Information |
|---|---|
| Book | Ganita Manjari: Textbook of Mathematics for Grade 9, Part I |
| Chapter number | 1 |
| Chapter name | Orienting Yourself: The Use of Coordinates |
| Starting page | Page 1 |
| Exercise Sets | Exercise Set 1.1 and Exercise Set 1.2 |
| Extra practice | End of Chapter Exercises |
| Main formulas | Distance formula and midpoint formula |
| Session | 2026-27 |
What This Chapter Is About
Before this chapter, you described a place in words. “The chair is near the window.” That is not exact. Two people can read it in two different ways.
Coordinates fix this problem. You fix a starting point, called the origin. You draw two number lines through it, one across and one up. Now every point on the page has one exact address, written as a pair of numbers.
The chapter opens with how this idea grew. Cities in the Sindhu-Sarasvati civilisation were built on street grids. Later Indian mathematicians such as Baudhayana, Aryabhata and Brahmagupta worked with position and distance long before the Cartesian plane was written down in Europe in 1637.
The chapter then uses a simple story. A student maps his own room on a grid so he can find everything in it. From that everyday idea, the formal rules are built up step by step.
Chapter 1 Video Lesson – Extramarks Shaurya Series
Prefer to watch instead of read? In this Shaurya Series session, Swati Ma’am explains Orienting Yourself: The Use of Coordinates from the very beginning, in simple language.
Class 9 Maths | Chapter 1 | Ganita Manjari | The Use of Coordinates | Shaurya Series
This is Part I of the topic. The Shaurya Series is built for Class 9 students and covers the full syllabus with strong concept building.
How to use the video: Watch it once from start to finish. Then open Exercise Set 1.1 below and try the questions yourself before checking the solutions.
Topics Covered in Chapter 1
| Section | What you learn |
|---|---|
| Why we need coordinates | How people described position before the Cartesian plane, including grid-based city planning in ancient India |
| The 2-D Cartesian plane | x-axis, y-axis, origin, and the four quadrants |
| Ordered pairs | Writing a point as (x, y) and why the order matters |
| Plotting and reading points | Marking a point on graph paper and reading a point off a diagram |
| Signs in each quadrant | Which coordinates are positive and which are negative |
| Distance between two points | The distance formula, built from the Baudhayana–Pythagoras theorem |
| Midpoint of a segment | Finding the point exactly halfway between two points |
| Collinear points | Checking whether three points lie on one straight line |
| Real-life use | Room plans, city street grids, maps and screen coordinates |
The Four Quadrants
The two axes cut the plane into four parts. These are called quadrants. They are numbered anticlockwise, starting from the top right.
| Quadrant | x-coordinate | y-coordinate | Example point |
|---|---|---|---|
| Quadrant I | positive | positive | (4, 3) |
| Quadrant II | negative | positive | (−4, 3) |
| Quadrant III | negative | negative | (−4, −3) |
| Quadrant IV | positive | negative | (4, −3) |
Remember: a point on the x-axis is written (a, 0). A point on the y-axis is written (0, b). The origin is (0, 0). Points on an axis do not belong to any quadrant.
Formulas You Must Know
Chapter 1 has only two formulas. Both are easy once you see where they come from.
1. Distance between two points
For points A(x₁, y₁) and B(x₂, y₂):
AB = √[(x₂ − x₁)² + (y₂ − y₁)²]
This is just the Baudhayana–Pythagoras theorem. Draw a right-angled triangle with AB as the slanting side. The bottom side is (x₂ − x₁) and the upright side is (y₂ − y₁). Square both, add, take the square root.
2. Midpoint of a line segment
For points A(x₁, y₁) and B(x₂, y₂):
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The midpoint is simply the average of the two x-values and the average of the two y-values.
Solved Examples from Chapter 1
Example 1: Reading a point
Question. A point lies 6 units to the left of the y-axis and 4 units below the x-axis. Write its coordinates and name its quadrant.
Solution.
Left of the y-axis means the x-value is negative, so x = −6.
Below the x-axis means the y-value is negative, so y = −4.
The point is (−6, −4).
Both values are negative, so it lies in Quadrant III.
Example 2: Using the distance formula
Question. Find the distance between P(2, 3) and Q(7, 15).
Solution.
PQ = √[(7 − 2)² + (15 − 3)²]
= √[5² + 12²]
= √(25 + 144)
= √169
= 13 units
Example 3: Using the midpoint formula
Question. M(4, −1) is the midpoint of A(1, 5) and B. Find B.
Solution.
Let B be (x, y).
For the x-value: (1 + x)/2 = 4, so 1 + x = 8, so x = 7.
For the y-value: (5 + y)/2 = −1, so 5 + y = −2, so y = −7.
Therefore B is (7, −7).
Example 4: Checking collinear points
Question. Do the points A(0, 0), B(3, 4) and C(6, 8) lie on one straight line?
Solution.
AB = √(3² + 4²) = √25 = 5
BC = √(3² + 4²) = √25 = 5
AC = √(6² + 8²) = √100 = 10
Now check: AB + BC = 5 + 5 = 10 = AC.
The two shorter distances add up to the longest one, so A, B and C are collinear.
Chapter 1 Exercise-wise NCERT Solutions
Every question is solved step by step, with the reason for each step. Click the exercise you need.
| Exercise | What it covers | Solutions |
|---|---|---|
| Exercise Set 1.1 | Reading coordinates from a room plan, distances along the axes | View solutions |
| Exercise Set 1.2 | Plotting points on graph paper, completing shapes, working in all four quadrants | View solutions |
| End of Chapter Exercises | Distance formula, midpoints, collinearity, circles and city-grid problems | View solutions |
Study tip: do Exercise Set 1.1 and 1.2 first. They build the method. The End of Chapter Exercises then mix everything together, which is closer to how exam questions are set.
Common Mistakes in Chapter 1
| Mistake | How to avoid it |
|---|---|
| Writing (y, x) instead of (x, y) | Say it aloud: “across first, then up”. The x-value always comes first. |
| Mixing up signs in Quadrants II and III | Draw the four quadrants in the margin of your rough sheet before you start. |
| Forgetting the square root in the distance formula | Distance is always √(…). If you stop at the squared value, you have the answer to a different question. |
| Adding coordinates instead of averaging for a midpoint | Midpoint means average. Divide each sum by 2. |
| Losing marks on graph questions | Label both axes, mark the scale, and name each plotted point. |
| Treating a negative distance as an answer | Distance can never be negative. If you get one, check your subtraction order. |
How to Study Chapter 1
- Keep graph paper ready. This chapter cannot be learnt by reading alone. Plot every point yourself.
- Draw the quadrant signs once. Sketch the four quadrants with their signs at the top of your notebook page. Look at it until you no longer need to.
- Derive the distance formula once. Draw the right-angled triangle and work it out. After that you will never forget it.
- Say “across, then up”. This one habit prevents the most common mistake in the whole chapter.
- Check answers against the picture. If your calculated distance is 13 units but the two points look 3 units apart on your graph, you have made an arithmetic slip.
- Then attempt the star-marked questions. They are not in the exam, but they build the reasoning the exam rewards.
Why Chapter 1 Matters Later
- Chapter 2 draws linear polynomials as straight lines on this same plane.
- Chapter 3 places rational and irrational numbers on the number line, which is one axis of this plane.
- Chapter 5 uses coordinates to describe circles and points on them.
- Class 10 extends this chapter with the section formula and the area of a triangle from coordinates.
Related Study Material
FAQs (Frequently Asked Questions)
Chapter 1 is Orienting Yourself: The Use of Coordinates. It is the first chapter of the new NCERT Class 9 Maths book. It teaches the Cartesian plane, plotting points, the distance formula and the midpoint formula.
There are two Exercise Sets, 1.1 and 1.2, plus one set of End of Chapter Exercises. All three are solved on Extramarks.
The old book started with Number Systems. Ganita Manjari starts with coordinates because graphs and coordinate thinking are used again in Chapter 2 (linear polynomials) and Chapter 3 (the number line). Starting here makes the later chapters easier.
Yes. The distance formula is taught inside Chapter 1 in the new book and is used in the End of Chapter Exercises. You should know how it is derived, not just how to use it.
The distance formula tells you how far apart two points are. The midpoint formula tells you the point exactly halfway between them. Distance uses subtraction and a square root. Midpoint uses addition and division by 2.
No. The textbook says star-marked questions are for extra practice and deeper thinking. They are not part of formal assessment. They are still good practice if you have time.
Find the distance between each pair of points. If the two shorter distances add up to the longest one, the three points are collinear, which means they lie on one straight line.
Chapter 2, Introduction to Linear Polynomials. It uses the graph work from Chapter 1, so finish this chapter properly before moving on.