NCERT Solutions for Class 9 Maths Chapter 1 Orienting Yourself the Use of Coordinates provide clear, step-by-step answers to every exercise and in-text question from the chapter Orienting Yourself the Use of Coordinates of the NCERT textbook Ganita Manjari. Prepared by subject experts as per the latest NCERT (CBSE) syllabus for 2026-27, these NCERT Solutions for Class 9 Maths help you understand each concept, write exam-ready answers, and check your own solutions. You can read them online below or download the free Class 9 Maths Chapter 1 question-answer PDF.
NCERT Solutions for Class 9 Maths Chapter 1 Orienting Yourself the Use of Coordinates
- Class: Class 9
- Subject: Maths
- Chapter: Chapter 1 – Orienting Yourself the Use of Coordinates
- Textbook: Ganita Manjari (NCERT)
- Study material: NCERT Solutions – questions with answers, free PDF
These solutions answer all the exercise questions of Chapter 1 Orienting Yourself the Use of Coordinates — including the in-text questions, short-answer and long-answer questions, and activities — with complete explanations so you can follow the method, not just the final answer. Read the full solutions below.
NCERT Solutions Class 9 Maths Chapter 1 Orienting Yourself the Use of Coordinates View Download
NCERT Solutions for Class 9 Maths Chapter 1 PDF Download
You can read the NCERT Solutions for Class 9 Maths Chapter 1 online above, or download the complete question-answer PDF to study Orienting Yourself the Use of Coordinates offline at any time.
NCERT Solutions for Class 9 Maths Chapter 1 PDF Download Link – Click Here to Download Solutions PDF
Questions Covered in This Chapter
These NCERT Solutions answer all 39 questions of this chapter. The questions solved are:
- Notice that this only shows the map of the floor. Do you see why the position of the windows cannot be marked on this map?
- If D₁R₁ represents the door to Reiaan’s room, how far is the door from the left wall (the y-axis) of the room? How far is the door from the x-axis?
- What are the coordinates of D₁?
- If R₁ is the point (11.5, 0), how wide is the door? Do you think this is a comfortable width for the room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily?
- If B₁ (0, 1.5) and B₂ (0, 4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?
- What are the standard widths for a room door? Look around your home and in school.
- Are the doors in your school suitable for people in wheelchairs?
- So far, we have only considered points on the two coordinate axes. What can you say about the coordinates of points that are not on either axes?
- Copy Fig. 1.4 and mark S and Q in your diagram. Mark any point P in Quadrant I and any point R in Quadrant III, and write down their coordinates.
- What is the x-coordinate of a point on the y-axis?
- Is there a similar generalisation for a point on the x-axis?
- Does point Q (y, x) ever coincide with point P (x, y)? Justify your answer.
- If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true?
- Place Reiaan’s rectangular study table with three of its feet at the points (8, 9), (11, 9) and (11, 7). (i) Where will the fourth foot of the table be? (ii) Is this a good spot for the table? (iii) What is the width of the table? The length? Can you make out the height of the table?
- If the bathroom door has a hinge at B₁ and opens into the bedroom, will it hit the wardrobe? Are there any changes you would suggest if the door is made wider?
- Look at Reiaan’s bathroom. (i) What are the coordinates of the four corners O, F, R, and P of the bathroom? (ii) What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners. (iii) Mark off a 3 ft × 2 ft space for the washbasin and a 2 ft × 3 ft space for the toilet. Write the coordinates of the corners of these spaces.
- Other rooms in the house: (i) Reiaan’s room door leads from the dining room which has the length 18 ft and width 15 ft. The length of the dining room extends from point P to point A. Sketch the dining room and mark the coordinates of its corners. (ii) Place a rectangular 5 ft × 3 ft dining table precisely in the centre of the dining room. Write down the coordinates of the feet of the table.
- Triangle ADM is an acute angled triangle in the first quadrant. How do we find the lengths of its sides AD, DM and MA?
- In moving from A (3, 4) to D (7, 1), what distance has been covered along the x-axis? What about the distance along the y-axis?
- Can these distances help you find the distance AD?
- What if, x₁, x₂, y₁, y₂ take negative values? In Fig. 1.9, triangle AMD is reflected in the y-axis. What are the coordinates of the images of points A, M, and D?
- What has remained the same and what has changed with this reflection?
- Would these observations be the same if ΔADM is reflected in the x-axis (instead of the y-axis)?
- What are the x-coordinate and y-coordinate of the point of intersection of the two axes?
- Point W has x-coordinate equal to − 5. Can you predict the coordinates of point H which is on the line through W parallel to the y-axis? Which quadrants can H lie in?
- Consider the points R (3, 0), A (0, − 2), M (− 5, − 2) and P (− 5, 2). If they are joined in the same order, predict: (i) Two sides of RAMP that are perpendicular to each other. (ii) One side of RAMP that is parallel to one of the axes. (iii) Two points that are mirror images of each other in one axis. Which axis will this be? Now plot the points and verify your predictions.
- Plot point Z (5, − 6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides. (Comment: Answers may differ from person to person.)
- What would a system of coordinates be like if we did not have negative numbers? Would this system allow us to locate all the points on a 2-D plane?
- Are the points M (− 3, − 4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method to check this without plotting and joining the points.
- Use your method (from Problem 6) to check if the points R (− 5, − 1), B (− 2, − 5) and C (4, − 12) are on the same straight line. Now plot both sets of points and check your answers.
- Using the origin as one vertex, plot the vertices of: (i) A right-angled isosceles triangle. (ii) An isosceles triangle with one vertex in Quadrant III and the other in Quadrant IV.
- The following table shows the coordinates of points S, M and T. In each case, state whether M is the midpoint of segment ST. Justify your answer. [S, M, T: (−3, 0), (0, 0), (3, 0) | (2, 3), (3, 4), (4, 5) | (0, 0), (0, 5), (0, −10) | (−8, 7), (0, −2), (6, −3)] When M is the mid-point of ST, can you find any connection between the coordinates of M, S and T?
- Use the connection you found to find the coordinates of B given that M (−7, 1) is the midpoint of A (3, − 4) and B (x, y).
- Let P, Q be points of trisection of AB, with P closer to A, and Q closer to B. Using your knowledge of how to find the coordinates of the midpoint of a segment, how would you find the coordinates of P and Q? Do this for the case when the points are A (4, 7) and B (16, −2).
- (i) Given the points A (1, − 8), B (− 4, 7) and C (−7, − 4), show that they lie on a circle K whose center is the origin O (0, 0). What is the radius of circle K? (ii) Given the points D (− 5, 6) and E (0, 9), check whether D and E lie within the circle, on the circle, or outside the circle K.
- The midpoints of the sides of triangle ABC are the points D, E, and F. Given that the coordinates of D, E, and F are (5, 1), (6, 5), and (0, 3), respectively, find the coordinates of A, B and C.
- A city has two main roads which cross each other at the centre of the city. These two roads are along the North–South (N–S) direction and East–West (E–W) direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 10 streets in each direction. (i) Using 1 cm = 200 m, draw a model of the city in your notebook. Represent the roads/streets by single lines. (ii) There are street intersections in the model. Each street intersection is formed by two streets — one running in the N–S direction and another in the E–W direction. Each street intersection is referred to in the following manner: If the second street running in the N–S direction and 5th street in the E–W direction meet at some crossing, then we call this street intersection (2, 5). Using this convention, find: (a) how many street intersections can be referred to as (4, 3). (b) how many street intersections can be referred to as (3, 4).
- A computer graphics program displays images on a rectangular screen whose coordinate system has the origin at the bottom-left corner. The screen is 800 pixels wide and 600 pixels high. A circular icon of radius 80 pixels is drawn with its centre at the point A (100, 150). Another circular icon of radius 100 pixels is drawn with its centre at the point B (250, 230). Determine: (i) whether any part of either circle lies outside the screen. (ii) whether the two circles intersect each other.
- Plot the points A (2, 1), B (−1, 2), C (−2, −1), and D (1, −2) in the coordinate plane. Is ABCD a square? Can you explain why? What is the area of this square?
Chapter at a Glance
- Two perpendicular number lines — the horizontal x-axis and the vertical y-axis — meet at the origin O (0, 0). Together they are the coordinate axes, and the plane they lie in is the Cartesian plane (also: coordinate plane, xy-plane).
- For a point P ( x , y ), x is the perpendicular distance of P from the y-axis measured along the x-axis, and y is its perpendicular distance from the x-axis measured along the y-axis. Right and up are positive; left and down are negative.
- Because each of the two displacements carries its own sign, there are 2 × 2 = 4 sign patterns, and so exactly four quadrants : I (+, +), II (−, +), III (−, −), IV (+, −). A point with a zero displacement sits on an axis and belongs to no quadrant: ( x , 0) on the x-axis, (0, y ) on the y-axis.
- The pair is ordered . ( x , y ) = ( y , x ) only when x = y ; otherwise the two are different points, mirror images of each other in the line through O that bisects Quadrants I and III.
- Distances along a grid line are differences: | x 2 − x 1 | for a horizontal segment, | y 2 − y 1 | for a vertical one.
- For any two points, the horizontal and vertical shifts are the legs of a right triangle, so by the Baudhāyana–Pythagoras Theorem the distance is √(( x 2 − x 1 )² + ( y 2 − y 1 )²). Squaring removes the signs, so it does not matter which point is called first.
How to Download NCERT Solutions for Class 9 Maths Chapter 1 PDF
Follow these simple steps to get the Orienting Yourself the Use of Coordinates questions-and-answers PDF from Ganita Manjari.
- Search NCERT Solutions for Class 9 Maths Chapter 1 aglasem and open this page.
- Read the exercise questions with answers for Orienting Yourself the Use of Coordinates shown above.
- Click the Download PDF link to save the Orienting Yourself the Use of Coordinates solutions to your device.
NCERT Solutions for Class 9 Maths – All Chapters
There are more chapters to study besides Orienting Yourself the Use of Coordinates in Maths. Here are the NCERT Solutions for all chapters of Class 9 Maths.
- Chapter 1 Orienting Yourself the Use of Coordinates
- Chapter 2 Introduction to Linear Polynomials
- Chapter 3 The World of Numbers
- Chapter 4 Exploring Algebraic Identities
- Chapter 5 I M Up and Down and Round and Round
- Chapter 6 Measuring Space Perimeter and Area
- Chapter 7 The Mathematics of Maybe Introduction to Probability
- Chapter 8 Predicting What Comes Next Exploring Sequences and Progressions
NCERT Solutions for Class 9 – All Subjects
Just like Chapter 1 of Maths, you can get the exercise questions with answers for every other subject of Class 9. Here are the NCERT Solutions for all subjects of Class 9.
NCERT Solutions for Class 9 Maths Chapter 1 – An Overview
The key highlights of this study material are as follows.
| Aspects | Details |
|---|---|
| Class | Class 9 |
| Subject | Maths |
| Chapter Number | Chapter 1 |
| Chapter Name | Orienting Yourself the Use of Coordinates |
| Book Name | Ganita Manjari |
| Book By | NCERT (National Council of Educational Research and Training) |
| Educational Resource Here | NCERT Solutions of Class 9 Maths Chapter 1 for all exercises |
| More Questions Answers of This Subject | NCERT Solutions for Class 9 Maths |
| Download Book Chapter | NCERT Book Class 9 Maths |
| All Questions Answers For This Class | NCERT Solutions for Class 9 |
| Complete Solutions | NCERT Solutions |
NCERT Solutions for Class 9 Maths Chapter 1 Orienting Yourself the Use of Coordinates – FAQs
What are the NCERT Solutions for Class 9 Maths Chapter 1 Orienting Yourself the Use of Coordinates?
They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 1 Orienting Yourself the Use of Coordinates from the NCERT Class 9 Maths textbook Ganita Manjari, written by experts as per the latest NCERT syllabus.
How can I download the Class 9 Maths Chapter 1 solutions PDF for free?
Open this page on aglasem, read the Orienting Yourself the Use of Coordinates questions with answers, and click the “Download Solutions PDF” link. The Class 9 Maths Chapter 1 NCERT Solutions PDF is completely free to download.
Are these NCERT Solutions as per the latest 2026-27 syllabus?
Yes. The NCERT Solutions for Class 9 Maths Chapter 1 are based on the latest NCERT textbook Ganita Manjari and the current 2026-27 CBSE syllabus, so the questions and answers match what you study in class.
Where can I get NCERT Solutions for the other chapters of Class 9 Maths?
You can find the answers to every chapter on the NCERT Solutions for Class 9 Maths page, and solutions for every subject on the NCERT Solutions for Class 9 page.
How do NCERT Solutions help in exam preparation?
They show the correct method to solve each question, help you write answers the way they are expected in exams, let you check and correct your own work, and save revision time — which together improve your marks in Class 9 Maths.
If you have any queries on NCERT Solutions for Class 9 Maths Chapter 1 Orienting Yourself the Use of Coordinates, then please ask in the comments below.
