Coordinate Geometry
NCERT Solutions • Class 9 Maths • Chapter 3Exercise 3.1
1. How will you describe the position of a table lamp on your study table to another person?
To describe the position of the table lamp, we can use the concept of a Coordinate System.
Steps:
Example: If the lamp is 20 cm from the left edge and 30 cm from the bottom edge, the position is $(20, 30)$.
Steps:
- Consider the table surface as a plane.
- Take any two perpendicular edges of the table as the axes (say, the longer edge as the X-axis and the shorter edge as the Y-axis).
- Measure the distance of the lamp from the shorter edge (Y-axis). Let it be $a$ cm.
- Measure the distance of the lamp from the longer edge (X-axis). Let it be $b$ cm.
- The position of the lamp can be described as the coordinate point:
Position: (a, b) or Position: (b, a)
Example: If the lamp is 20 cm from the left edge and 30 cm from the bottom edge, the position is $(20, 30)$.
2. (Street Plan): A city has two main roads which cross each other at the centre… Using 1cm = 200 m, draw a model. Find:
Understanding the Model:
The two main roads act as the X-axis (East-West) and Y-axis (North-South). The crossing point is the Origin (0,0).
A cross-street is denoted by $(x, y)$, where:
• $x$ = Street number running North-South (Vertical).
• $y$ = Street number running East-West (Horizontal).
The two main roads act as the X-axis (East-West) and Y-axis (North-South). The crossing point is the Origin (0,0).
A cross-street is denoted by $(x, y)$, where:
• $x$ = Street number running North-South (Vertical).
• $y$ = Street number running East-West (Horizontal).
(i) How many cross-streets can be referred to as (4, 3)?
Since a coordinate $(x, y)$ represents a unique point on the Cartesian plane, there is only one specific intersection where the 4th North-South street meets the 3rd East-West street.
Answer: There is only 1 cross-street referred to as $(4, 3)$.
Since a coordinate $(x, y)$ represents a unique point on the Cartesian plane, there is only one specific intersection where the 4th North-South street meets the 3rd East-West street.
Answer: There is only 1 cross-street referred to as $(4, 3)$.
(ii) How many cross-streets can be referred to as (3, 4)?
Similarly, the intersection of the 3rd North-South street and the 4th East-West street corresponds to a unique point. The order of coordinates matters in Cartesian geometry ($(x, y) \neq (y, x)$ unless $x=y$).
Answer: There is only 1 cross-street referred to as $(3, 4)$.
Similarly, the intersection of the 3rd North-South street and the 4th East-West street corresponds to a unique point. The order of coordinates matters in Cartesian geometry ($(x, y) \neq (y, x)$ unless $x=y$).
Answer: There is only 1 cross-street referred to as $(3, 4)$.