Chapter 5: Co-ordinate Geometry (Exercise 5.1)

Chapter 5: Co-ordinate Geometry (Exercise 5.1)

Question 1:
Write the answers of each of the following questions:
1. What is the name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?
2. What is the name of each part of the plane formed by these two lines?
3. Write the name of the point where these two lines intersect.

Solution:
1. The horizontal line is called the X-axis and the vertical line is called the Y-axis.
2. Each part of the plane formed by these two lines is called a Quadrant (Quadrant I, II, III, and IV).
3. The point of intersection of the X-axis and Y-axis is called the Origin (O) with coordinates (0, 0).

Question 2:
In the given Cartesian plane, write the coordinates of points A, B, C, and D.

Solution:
* Point A: Lies in Quadrant I, Abscissa = 4, Ordinate = 3 ⇒ (4, 3)
* Point B: Lies in Quadrant II, Abscissa = -4, Ordinate = 3 ⇒ (-4, 3)
* Point C: Lies in Quadrant III, Abscissa = -4, Ordinate = -3 ⇒ (-4, -3)
* Point D: Lies in Quadrant IV, Abscissa = 3, Ordinate = -3 ⇒ (3, -3)

Question 3:
In which quadrant or on which axis do each of the points (-2, 4), (3, -1), (-1, 0), (1, 2), and (-3, -5) lie?

Solution:
* (-2, 4): Lies in Quadrant II (X is negative, Y is positive).
* (3, -1): Lies in Quadrant IV (X is positive, Y is negative).
* (-1, 0): Lies on the Negative X-axis (Y-coordinate is 0).
* (1, 2): Lies in Quadrant I (Both X and Y are positive).
* (-3, -5): Lies in Quadrant III (Both X and Y are negative).