Orienting Yourself: The Use of Coordinates Class 9 (Ganita Manjari)
Master Orienting Yourself: The Use of Coordinates Class 9 (Ganita Manjari) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
NCERT Solutions
Orienting Yourself: The Use of Coordinates Class 9 (Ganita Manjari) – NCERT Solutions
Each question below opens its complete step-by-step Teachoo solution.
Exercise Set 1.1
4 questionsEx 1.1, 1 (i)
Fig. 1.3 shows Reiaan’s room with points OABC marking its corners. The x- and y-axes are marked in the figure. Point O is the origin.
View solutionEx 1.1, 1 (ii)
What are the coordinates of D1?
To find the coordinates, we always use the format (x, y).
As we found in the previous step, D₁ is at the 8 mark on the horizontal x-axis. This means our x-coordinate is 8.
Since the point sits directly on the x-axis and hasn't moved up or down, the vertical y-coordinate is 0.
Ex 1.1, 1 (iii)
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?
The door spans along the x-axis from D₁ at (8, 0) to R₁ at (11.5, 0).
To find the width, we just subtract the smaller x-coordinate from the larger x-coordinate:
Width of door = 11.5 – 8
= 3.5 units
Ex 1.1, 1 (iv)
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?
The bathroom door lies on the y-axis (the left wall) between point B₁ at (0, 1.5) and point B₂ at (0, 4).
To find its width, we subtract the smaller y-coordinate from the larger y-coordinate:
Width of bathroom door = 4 – 1.5
= 2.5 units
Exercise Set 1.2
4 questionsEx 1.2, 1
On a graph sheet, mark the x-axis and y-axis and the origin O. Mark points from (– 7, 0) to (13, 0) on the x-axis and from (0, – 15) to
(0, 12) on the y-axis. (Use the scale 1 cm = 1 unit.) Using Fig. 1.5, answer the given questions.
Let’s plot the graph
Ex 1.2, 1 (i) 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?
Let’s plot the points in Fig 1.5.
Ex 1.2, 2
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?
Let’s make a line joining B1 and B2, and then open it from B1 Horizontally
From the figure we can see that the Bathroom door doesn’t hit the wardrobe.
Ex 1.2, 3
(i) Look at Reiaan’s bathroom.
What are the coordinates of the four corners O, F, R, and P of the bathroom?
Let’s mark the coordinates
Let’s find the coordinates
𝑶 (bottom-right): (0,0)
F (top-right): Looking at the 𝑦-axis, point 𝐹 is at 9 . (0, 9)
𝑷 (bottom-left): Looking at the x -axis, point P is deep into negative territory. (−6,0)
𝑹 (top-left): This aligns with P on the x -axis and F on the 𝑦-axis. (−6,9)
Ex 1.2, 4
(i) Other rooms in the house:
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.
Let’s draw this
Given that Dining room has Length = 18ft, Width = 15ft
The text says the length extends from P(−6, 0) to A (12, 0).
Let's verify: 12−(−6)=18 feet.
End-of-Chapter Exercises
16 questionsQuestion 1
What are the x-coordinate and y-coordinate of the point of intersection of the two axes?
Let’s draw the two axes, x-axis and y-axis
Question 2
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?
Let’s draw the Cartesian plane
Question 3
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.
Question 4
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.)
We follow this process
We plot point Z (5, –6)
We now draw two lines – one vertical from point Z and one horizonal
Let’s assume vertical point is 4 units above Z
And horizontal point is 3 units on the left side of Z
Question 5
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?
Let’s look at our cartesian graph and see
Question 6
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.
If three points are on the exact same straight line (collinear), then
Distance of the two shorter segments added together will perfectly equal the distance of the longest segment.
Question 7
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.
If three points are on the exact same straight line (collinear), then
Distance of the two shorter segments added together will perfectly equal the distance of the longest segment.
Question 8
(i) Using the origin as one vertex, plot the vertices of:
(i) A right-angled isosceles triangle.
Since it is a right-angled isosceles triangle, we
Draw a vertical line of distance 5
And a horizontal line of same distance 5
Thus, ∆ AOB is the required right isosceles triangle with
OA = OB = 5 units
∠ AOB = 90°
Question 8 (ii) An isosceles triangle with one vertex in Quadrant III and the
other in Quadrant IV.
Here, we choose a point and then draw a mirror image
Let’s choose one point in Quadrant III as (–5, –4)
Then its mirror image in Quadrant IV is (5, –4)
Thus, ∆ AOB is the required isosceles triangle with
OM = ON (their distance would be equal by distance formula)
Question 9
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
View solutionQuestion 10
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).
Formula for finding mid-point is
Mid-point of (x1, y1) & (x2, y2) = ((𝒙_𝟏 + 𝒙_𝟐)/𝟐,(𝒚_𝟏+𝒚_𝟐)/𝟐)
Question 11
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).
Let’s draw the figure
Question 12
(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?
Let’s draw a diagram
Question 13
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.
We draw a diagram
Let A (x1, y1) , B (x2, y2), C (x3, y3)
Question 14
(a) 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:
how many street intersections can be referred to as (4, 3).
(b) how many street intersections can be referred to as (3, 4).
Let’s first draw the streets in North-South and East-West Direction
The grids form a graph like in coordinate geometry
In coordinate geometry, the numbers (x, y) represents one specific, unique point in a 2-D plane.
Now, answering our questions
Question 15
(i) 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:
whether any part of either circle lies outside the screen.
whether the two circles intersect each other.
Let’s draw the Screen and the circles
Here,
Width can be considered as x-axis
Height can be considered as y-axis
And, we only work in Quadrant 1
Rectangular Screen 800 × 600 pixels
From the diagram we can see that
(i) - both circles lie fully inside the screen
(ii) - both circles intersect
Question 16
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?
Let’s plot the points
In a square,
All sides are equal
All diagonals are equal
Why Learn This With Teachoo?
Orienting Yourself: The Use of Coordinates is Chapter 1 of the new NCERT Class 9 Maths book Ganita Manjari Part 1. It explains how ordered pairs locate points in a plane and how coordinates can be used to describe position, distance and division of a line segment. Students learn the Cartesian coordinate system, quadrants, the distance formula, midpoint formula and section formula. Teachoo provides concept-wise explanations and step-by-step solutions for Exercise Sets 1.1 and 1.2 and the end-of-chapter exercises.
Understanding the coordinate system
A coordinate system converts geometric position into numerical information. Two perpendicular number lines form the Cartesian plane. The horizontal line is the x-axis, the vertical line is the y-axis and their intersection is the origin O(0, 0). A point is written as an ordered pair (x, y), where x gives horizontal displacement and y gives vertical displacement.
The first coordinate is called the x-coordinate or abscissa, and the second is the y-coordinate or ordinate. Their order cannot be interchanged: (3, 5) and (5, 3) usually represent different points. Points on the x-axis have y = 0, while points on the y-axis have x = 0.
Quadrants and signs of coordinates
The axes divide the plane into four quadrants. In Quadrant I, both coordinates are positive. In Quadrant II, x is negative and y is positive. In Quadrant III, both are negative. In Quadrant IV, x is positive and y is negative. Students identify a point’s quadrant, plot coordinates accurately and infer coordinate signs from a location.
Coordinate grids appear in maps, navigation, computer graphics, data visualisation and game design. The chapter title “Orienting Yourself” highlights this practical purpose: coordinates establish a reference system for saying exactly where something is.
Distance, midpoint and section formula
The distance between points A(x₁, y₁) and B(x₂, y₂) is
d = √[(x₂ − x₁)² + (y₂ − y₁)²].
This formula follows from the Baudhāyana–Pythagoras theorem by treating the horizontal and vertical coordinate differences as perpendicular sides of a right triangle. Distance is non-negative and remains the same if the points are reversed.
The midpoint of AB is ((x₁ + x₂)/2, (y₁ + y₂)/2). More generally, the section formula locates a point dividing a line segment in a specified ratio. The coordinates are weighted according to the opposite parts of the ratio, so the order of endpoints and ratio terms must be handled carefully.
Topics covered on Teachoo
Teachoo includes:
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the Cartesian coordinate system;
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origin, axes, abscissa and ordinate;
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plotting and reading ordered pairs;
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Exercise Set 1.1;
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four quadrants and coordinate signs;
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Exercise Set 1.2;
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distance between two points in a two-dimensional plane;
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midpoint and section formulas; and
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end-of-chapter exercise solutions.
Learning outcomes
Students should be able to plot and read points, identify quadrants and determine the signs of unknown coordinates. They should calculate distance, midpoint and a point dividing a segment in a given ratio and derive the distance formula from a right triangle. They should also translate a map, grid or geometric situation into coordinates and test whether a result is spatially reasonable.
Why is this chapter important?
Coordinate geometry unifies algebra and geometry. A geometric shape becomes a collection of ordered pairs, while length and division become algebraic calculations. These ideas support straight lines, graphs, transformations, analytic geometry, vectors, physics and computing.
How Teachoo helps you study
Teachoo separates coordinate basics from formula-based applications. Begin by plotting points manually on equally scaled axes. Mark x first and y second. For distance questions, calculate Δx and Δy separately before squaring. For midpoint or section questions, write the formula and substitute in the same endpoint order.
Attempt each exercise without seeing the final graph or result. Then use Teachoo to compare the plotted location, substitution and simplification. A correct number with an incorrectly identified quadrant is not a complete coordinate answer.
Common mistakes to avoid
Do not swap x and y. Negative coordinates indicate direction from the origin, not negative physical distance. In the distance formula, square the entire coordinate difference. Do not add the coordinates before subtracting, and do not omit the square root. For the section formula, match the ratio with the correct opposite endpoint weights.
Deeper reasoning and concept connections
A student has understood Orienting Yourself: The Use of Coordinates (Ganita Manjari) only when the idea can be moved between words, diagrams, examples and mathematical notation. Start with a concrete example, identify what changes and what remains fixed, represent the relationship clearly and then state the rule. This movement between representations is important because school and competency questions often present a familiar idea in an unfamiliar form.
The chapter should also be connected to earlier and later mathematics. Definitions supply the language, worked examples reveal the method, and mixed questions test whether the method can be selected without a hint. Instead of memorising the appearance of a solved question, ask what information triggered the method, which condition made it valid and how the answer could be checked. That makes learning transferable to later chapters rather than limited to one exercise.
How to solve unfamiliar and competency-based questions
Read the complete problem before calculating. Underline the quantities, conditions and command word—find, compare, construct, justify, estimate or prove. Rephrase the task in one sentence and choose a representation such as a table, labelled figure, number line, expression or graph. Solve in small steps, keeping units and labels visible.
For an application question, the final line must answer the situation, not only display a number. For an assertion–reason question, test the assertion and reason separately before deciding whether one explains the other. For an MCQ, eliminate options using definitions, signs, size estimates or boundary cases before performing long calculations. If the answer is visual, check it against the stated scale or construction conditions rather than the appearance of the drawing.
What complete mastery looks like
For Orienting Yourself: The Use of Coordinates (Ganita Manjari), a student should be able to define the central ideas in simple language, recognise them in different representations, solve routine questions accurately and explain the method used. They should also be able to correct a flawed solution, create an example satisfying given conditions and combine two ideas from the chapter in one problem. A reliable mastery test is to solve one direct question, one application question and one reasoning question without looking at notes, then explain all three aloud or in writing.
Keep a compact error log with four labels: concept, interpretation, calculation and presentation. Reattempt each error after a gap instead of rereading the answer immediately. Improvement comes from correcting the decision that caused the mistake, not from repeating questions whose method is already known.
Additional frequently asked questions
What should a student know before starting Orienting Yourself: The Use of Coordinates (Ganita Manjari)?
Revise the definitions, number operations, diagrams or notation used at the beginning of the chapter. The prerequisite list should be short: if an earlier skill blocks progress, repair that skill with two or three focused questions and return to the chapter.
How can a student check an answer in Orienting Yourself: The Use of Coordinates (Ganita Manjari)?
Use an independent check whenever possible: substitute the result, reverse the operation, estimate its size, compare it with the figure, test a simpler case or solve using another representation. A check should examine the mathematical condition, not merely repeat the same arithmetic.
How many questions are enough for strong preparation?
There is no fixed number. Stop counting questions and track coverage: every concept, every standard method, at least one mixed problem, one competency-based problem and every previously incorrect type should be solved independently. Ten varied, analysed questions are more valuable than fifty copied solutions.
How should Teachoo solutions be used without becoming dependent on them?
Attempt the question first and mark the exact step where progress stops. Read only enough of the solution to repair that step, close it and restart the question. Finally, solve a similar problem without help. This turns a solution into feedback rather than a substitute for thinking.
Frequently asked questions
What is an ordered pair?
It is a pair (x, y) in which the first value gives horizontal position and the second gives vertical position.
How do I know the quadrant of a point?
Check the signs of x and y: (+,+) is I, (−,+) is II, (−,−) is III and (+,−) is IV.
Why does the distance formula use the Pythagoras theorem?
The horizontal and vertical differences form perpendicular sides of a right triangle whose hypotenuse is the distance between the points.
Plot first, calculate second and check the answer against the geometry of the diagram.