Welcome back, Class 9 students! Today, we will explore the step-by-step solutions for Coordinate Geometry (Exercise 3.2) as per the MP Board / NCERT syllabus. This chapter is highly scoring and builds the foundation for advanced analytical geometry. Let's master the concepts of Cartesian planes, axes, and coordinates together!
NCERT / MP Board Class 9 Chapter 3 - Exercise 3.2
Question 1
Write the answer of each of the following questions:
- What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
- What is the name of each part of the plane formed by these two lines?
- Write the name of the point where these two lines intersect.
Solutions:
- (i) The horizontal line is called the x-axis, and the vertical line is called the y-axis.
- (ii) Each part of the plane formed by these two intersecting lines is called a quadrant (First, Second, Third, and Fourth quadrants).
- (iii) The point where these two lines intersect is called the origin (denoted by O, with coordinates (0, 0)).
Question 2
See the standard Cartesian figure (Fig 3.14 in your textbook) and write the following:
| S.No. | Question Requirement | Solution / Coordinates | Explanation |
|---|---|---|---|
| 1 | The coordinates of B | (-5, 2) | B lies 5 units to the left on the x-axis and 2 units up on the y-axis. |
| 2 | The coordinates of C | (5, -5) | C lies 5 units to the right on the x-axis and 5 units down on the y-axis. |
| 3 | The point identified by the coordinates (-3, -5) | Point E | Both coordinates are negative, putting it in Quadrant III. |
| 4 | The point identified by the coordinates (2, -4) | Point G | Abscissa is positive, ordinate is negative (Quadrant IV). |
| 5 | The abscissa of the point D | 6 | Abscissa is the x-coordinate of point D (6, 2). |
| 6 | The ordinate of the point H | -3 | Ordinate is the y-coordinate of point H (-5, -3). |
| 7 | The coordinates of the point L | (0, 5) | L lies on the y-axis, so its x-coordinate (abscissa) is 0. |
| 8 | The coordinates of the point M | (-3, 0) | M lies on the x-axis, so its y-coordinate (ordinate) is 0. |
ЁЯЪА Aptitude Corner (NTSE / Olympiad Edge)
Topic: Reflection of a Point and Coordinate Distance
In competitive exams like NTSE, you are often asked about the reflections of a point:
- Reflection in x-axis: Change the sign of the y-coordinate. Point (x, y) becomes (x, -y).
Example: Reflection of (-3, 5) in x-axis is (-3, -5). - Reflection in y-axis: Change the sign of the x-coordinate. Point (x, y) becomes (-x, y).
Example: Reflection of (-3, 5) in y-axis is (3, 5). - Reflection in Origin: Change the signs of both coordinates. Point (x, y) becomes (-x, -y).
Quick Challenge: Find the reflection of point P(4, -7) in the y-axis.
Answer: (-4, -7)
We hope this simple and structured breakdown of Exercise 3.2 helps you score full marks in your MP Board Term exams! Practice plotting these points on physical graph paper to visualize coordinate geometry better. Stay tuned for Exercise 3.3 solutions!
Academic Discussion & Doubts