NCERT Solutions for Class 9 Maths Chapter 1: Orienting Yourself – The Use of Coordinates by PW

Understanding coordinates becomes easier when you connect points on a coordinate plane with real-life locations and measurements. However, questions involving the x-axis, y-axis, coordinates, and distances can become confusing if you are not clear about how each point is represented and measured.

Class 9 Maths Ganita Manjari Chapter 1 Solutions by PW provide clear answers to the questions from Orienting Yourself: The Use of Coordinates. You can use these solutions to understand how coordinates help locate doors and other points, calculate distances, compare measurements, and apply coordinate concepts to practical situations.

Class 9 Maths Ganita Manjari Chapter 1 Solutions

The following solutions cover the questions related to Reiaan's room and the use of coordinates to represent the position and width of doors.

Question (i)

If D1R1D_1R_1 represents the door to Reiaan's room, how far is the door from the left wall (the yy-axis) of the room? How far is the door from the xx-axis?

Solution:

1. Distance from the left wall (yy-axis):

The point D1D_1 is located at x=8x=8.

Therefore, the door is 8 units away from the left wall, which is represented by the yy-axis.

2. Distance from the xx-axis:

The door lies along the xx-axis, where y=0y=0.

Therefore, the distance of the door from the xx-axis is 0 units.

Answer: The door is 8 units from the yy-axis and 0 units from the xx-axis.

Question (ii)

What are the coordinates of D1D_1?

Solution:

Point D1D_1 lies on the xx-axis at x=8x=8.

For every point on the xx-axis, the yy-coordinate is 00.

Therefore, the coordinates of D1D_1 are:

D1=(8,0)\boxed{D_1=(8,0)}

Answer: The coordinates of D1D_1 are (8,0)(8,0).

Question (iii)

If R1R_1 is the point (11.5,0)(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?

Solution:

1. Width of the door:

The points D1D_1 and R1R_1 lie on the xx-axis. Therefore, the width of the door is the difference between their xx-coordinates.

Width=11.5−8\text{Width}=11.5-8 Width=3.5 units\text{Width}=3.5\text{ units}

Therefore, the width of the room door is 3.5 units.

2. Is this a comfortable width?

The coordinate information tells us that the door is 3.5 units wide. Whether this is comfortable depends on the scale used in the diagram and the actual unit represented.

3. Can a wheelchair user enter easily?

The diagram alone does not provide enough information to determine wheelchair accessibility. It gives the door's width as 3.5 units, but accessibility would depend on the actual measurement represented by each unit and the required clearance.

Answer: The door is 3.5 units wide. Its comfort and accessibility cannot be determined from the coordinates alone without knowing the actual scale and relevant accessibility requirements.

Question (iv)

If B1(0,1.5)B_1(0,1.5) and B2(0,4)B_2(0,4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?

Solution:

The points B1B_1 and B2B_2 lie on the yy-axis. Therefore, the width of the bathroom door is the difference between their yy-coordinates.

Width=4−1.5\text{Width}=4-1.5 Width=2.5 units\text{Width}=2.5\text{ units}

So, the bathroom door is 2.5 units wide.

The room door is 3.5 units wide.

Since:

2.5<3.52.5<3.5

the bathroom door is narrower than the room door.

Answer: The bathroom door is narrower than the room door.

Class 9 Maths Ganita Manjari Chapter 1 Solutions PDF

Working through the questions in Orienting Yourself: The Use of Coordinates becomes easier with the Class 9 Maths Ganita Manjari Chapter 1 Solutions PDF. It includes solved answers that can help you understand coordinate-based calculations, verify your approach, and revise the main concepts from the chapter.

How Can NCERT Class 9 Maths Chapter 1 Solutions by PW Help You?

NCERT Class 9 Maths Chapter 1 Solutions by PW can support your revision by providing clear answers to coordinate-based questions and showing how mathematical measurements can be represented using points and axes.

• Understand Coordinates: Learn how points are represented using ordered pairs.

• Identify Points on Axes: Revise how points on the xx-axis and yy-axis are represented.

• Calculate Distances: Practise finding distances between points using their coordinates.

• Apply Coordinate Concepts: Connect coordinate geometry with practical examples such as room and door measurements.

• Compare Measurements: Learn how coordinate values can be used to compare different lengths.

• Check Calculations: Verify your answers after attempting the textbook questions yourself.

• Improve Problem-Solving: Follow the reasoning used to solve questions involving coordinates and measurements.

• Revise Chapter Concepts: Recall important ideas from Orienting Yourself: The Use of Coordinates before assessments.

Coordinates provide a useful way to locate points and represent measurements on a plane. The questions in Orienting Yourself: The Use of Coordinates show how these ideas can be applied to familiar situations. Working through the solutions can help you practise reading coordinates, calculating distances, and comparing measurements accurately.