Coordinate Geometry Questions Class 9th
Chapter 3 – Coordinate Geometry Questions HP Board
Question 1. What is the Cartesian coordinate system? Name its two axes.
Solution:
The Cartesian coordinate system is a system used to locate points on a plane using two numbers called coordinates.
It consists of two perpendicular number lines:
1. The horizontal axis is called the x-axis.
2. The vertical axis is called the y-axis.
These axes intersect at the origin, represented by O(0, 0).
Answer: The two axes are the x-axis and the y-axis.
Question 2. Write the coordinates of the origin.
Solution:
The origin is the point where the x-axis and y-axis intersect.
At the origin:
x-coordinate = 0
y-coordinate = 0
Therefore, the coordinates of the origin are (0, 0).
Answer: (0, 0)
Question 3. In which quadrant does the point (4, 5) lie?
Solution:
The coordinates of the given point are (4, 5).
Here:
x-coordinate = 4, which is positive.
y-coordinate = 5, which is positive.
A point with both coordinates positive lies in the first quadrant.
Answer: First quadrant (Quadrant I).
Question 4. Identify the quadrant in which the following points lie:
(a) (−3, 4)
(b) (5, −2)
(c) (−6, −7)
(d) (2, 3)
Solution:
The signs of coordinates in the four quadrants are:
First quadrant: (+, +)
Second quadrant: (−, +)
Third quadrant: (−, −)
Fourth quadrant: (+, −)
(a) (−3, 4): Second quadrant.
(b) (5, −2): Fourth quadrant.
(c) (−6, −7): Third quadrant.
(d) (2, 3): First quadrant.
Answer: (a) II, (b) IV, (c) III, (d) I.
Question 5. Where does a point lie if its x-coordinate is zero?
Solution:
If the x-coordinate of a point is zero, its coordinates are of the form (0, y).
Such a point lies on the y-axis.
For example, the point (0, 4) lies on the y-axis.
Answer: The point lies on the y-axis.
Question 6. Where does a point lie if its y-coordinate is zero?
Solution:
If the y-coordinate of a point is zero, its coordinates are of the form (x, 0).
Such a point lies on the x-axis.
For example, the point (5, 0) lies on the x-axis.
Answer: The point lies on the x-axis.
Question 7. Write the coordinates of a point that is 3 units to the right of the origin and 4 units above the origin.
Solution:
Moving 3 units to the right gives the positive x-coordinate, 3.
Moving 4 units above the origin gives the positive y-coordinate, 4.
Therefore, the coordinates are (3, 4).
Answer: (3, 4).
Question 8. Write the abscissa and ordinate of the point (−5, 7).
Solution:
The first coordinate of a point is called the abscissa.
The second coordinate is called the ordinate.
For the point (−5, 7):
Abscissa = −5
Ordinate = 7
Answer: Abscissa = −5; ordinate = 7.
Question 9. A point lies on the x-axis and is 6 units to the left of the origin. Find its coordinates.
Solution:
A point on the x-axis has a y-coordinate of zero.
Since the point is 6 units to the left of the origin, its x-coordinate is −6.
Therefore, the coordinates are (−6, 0).
Answer: (−6, 0).
Question 10. Plot the points A(2, 3), B(−2, 3), C(−2, −3) and D(2, −3) on the Cartesian plane. Name the figure formed by joining them in order.
Solution:
Plot the four points on the Cartesian plane:
A(2, 3) lies in the first quadrant.
B(−2, 3) lies in the second quadrant.
C(−2, −3) lies in the third quadrant.
D(2, −3) lies in the fourth quadrant.
Join A to B, B to C, C to D and D to A.
The opposite sides are parallel and equal, and all angles are right angles.
Answer: The figure formed is a rectangle.