Exercise 1.1 Class 9 Maths Solutions | Ganita Manjari
Welcome to Sid Classes, your trusted destination for comprehensive academic resources! In this detailed study guide, we present complete, step-by-step solutions for NCERT Class 9 Maths Ganita Manjari Chapter 1 Exercise 11 Orienting Yourself: The Use of Coordinates. Designed to reflect how top-scoring students write their solutions and reasoning in school examinations, this walkthrough covers basic coordinate geometry concepts, calculating distances, evaluating door widths, and determining wheelchair accessibility using ordered pairs on a graph.
🔑 Key Concepts & Principles:
- Coordinate Geometry Basics: Locating positions on a plane using perpendicular axes—the horizontal x-axis and vertical y-axis.
- Origin & Ordered Pairs: The intersection point of both axes is called the origin \((0,0)\). Points are defined by ordered pairs \((x, y)\).
NCERT Class 9 Maths Ganita Manjari Chapter 1 Exercise 1.1 Solutions
Question 1
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.
Referring to Fig. 1.3, answer the following questions:
(i) If \(D_1 R_1\) 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?
Solution:
* Point \(D_1\) is located at \((8, 0)\) and point \(R_1\) at \((11.5, 0)\). The x-coordinate of \(D_1\) is 8, which means the door is 8 units away from the left wall (the y-axis).
* Since both \(D_1\) and \(R_1\) lie directly on the x-axis (y-coordinate = 0), the door is 0 units away from the x-axis.
(ii) What are the coordinates of \(D_1\)?
Solution:
The coordinates of \(D_1\) are \((8, 0)\).
(iii) If \(R_1\) 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?
Solution:
* Width of the door: \(\text{Distance} = 11.5 - 8 = \mathbf{3.5\text{ units}}\).
* Yes, 3.5 units provides a very comfortable width for a room door.
* A person using a wheelchair can easily enter the room through this door without difficulty.
(iv) If \(B_1 (0, 1.5)\) and \(B_2 (0, 4)\) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?
Solution:
* Width of the bathroom door: \(\text{Distance} = 4 - 1.5 = \mathbf{2.5\text{ units}}\).
* Comparing the two widths: Since \(2.5\text{ units} < 3.5\text{ units}\), the bathroom door is narrower than the main room door.
Frequently Asked Questions (FAQs)
Q1. What is Exercise 1.1 Class 9 Maths about?
A: Exercise 1.1 introduces the basics of coordinate geometry, including axes, origin, coordinates, and locating points on a graph.
Q2. Are these Exercise 1.1 solutions based on the latest CBSE syllabus?
A: Yes, these step-by-step solutions are prepared according to the latest CBSE and NCERT Ganita Manjari syllabus.
Q3. Why is coordinate geometry important in Class 9 Maths?
A: Coordinate geometry helps students understand algebraic plotting, spatial awareness, and navigation, forming a core foundation for higher mathematics.
Q4. What is the origin in coordinate geometry?
A: The point where the x-axis and y-axis intersect is called the origin, represented by the ordered pair \((0, 0)\).
Q5. Where is coordinate geometry used in real life?
A: It is widely used in GPS navigation systems, architectural layouts, digital mapping, engineering designs, and computer graphics.
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Last updated according to the latest NCERT and CBSE syllabus.