NCERT MCQ Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

In the Cartesian system, the horizontal line is called the x-axis. It is drawn left to right and represents the direction of increasing or decreasing values of x. This axis, along with the y-axis, helps locate the position of any point in the coordinate plane.

The coordinate axes intersect at a point called the origin. It is the reference point from which all other coordinates are measured. At the origin, the x-coordinate and y-coordinate are both zero. Hence, its coordinates are written as (0, 0).

A point lies in the second quadrant if the x-coordinate is negative and the y-coordinate is positive. For (–3, 2), the x-value is negative and the y-value is positive, satisfying the condition for the second quadrant of the Cartesian plane.

Any point lying on the x-axis has a zero distance from the x-axis, so its y-coordinate is zero. Therefore, the coordinates of any point on the x-axis take the form (x, 0), where x is the distance from the origin along the x-axis.

In the Cartesian coordinate system, the vertical axis is called the y-axis. It is drawn up and down on the plane and helps measure the vertical position of a point. The positive y-axis is above the origin and the negative y-axis is below it.

Understanding the Given Point (-4, -3)
A point in the coordinate system is represented as (x,y), where: 
The first value represents the x-coordinate.
The second value represents the y-coordinate.
Given Point (-4, -3)
x = -4 (first value)
y = -3(second value)
Final Answer: x = -4, y = -3.

Understanding the Ordinate of Points on the X-Axis
In a coordinate plane:
The abscissa is the x-coordinate of a point (x,y).
The ordinate is the y-coordinate of a point (x,y).
Any point on the x-axis has a y-coordinate of 0, meaning its general form is (x,0).
Conclusion:
The ordinate (y-coordinate) of all points on the x-axis is always 0.
The x-coordinate (abscissa) can be any number, but the ordinate remains 0.
Final Answer: 0.

The y-coordinate of a point, which is its distance from the x-axis, is called the ordinate. This value indicates how far the point is vertically placed above or below the x-axis on the Cartesian plane.

The origin is the central point where both x-axis and y-axis intersect. Since the origin lies at zero distance from both axes, its coordinates are represented as (0, 0), which serves as the reference point for all coordinate locations.

In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative. Among the given options, only the point (3, –2) satisfies this condition, placing it in the fourth quadrant of the Cartesian plane.

A point with both coordinates negative lies in the third quadrant. In the case of (–4, –2), both x and y values are negative, confirming that it lies in the third quadrant of the coordinate system.

A point on the y-axis is located at a zero distance from the y-axis, meaning its x-coordinate is zero. Hence, the coordinates of such a point take the form (0, y), where y is the distance from the x-axis.

Determining the Quadrant of the Point (-3, -2)
In a coordinate plane, the quadrant of a point (x, y) is determined by the signs of its coordinates:
Quadrant I → (x > 0, y > 0)
Quadrant II → (x < 0, y > 0)

Quadrant III → (x < 0, y < 0) Quadrant IV → (x > 0, y < 0) Given Point: (-3 -2) The x-coordinate is -3 (negative). The y-coordinate is -2 (negative). Since both x and y are negative, the point lies in Quadrant III. Final Answer: Quadrant III.

Determining the Quadrant of Given Points
A point (x, y) lies in a specific quadrant based on the signs of its coordinates:
Quadrant I → (x > 0, y > 0)
Quadrant II → (x < 0, y > 0)
Quadrant III → (x < 0, y < 0) Quadrant IV → (x > 0, y < 0) Analyzing Each Point 1. Point (1 , -2) x = 1 (positive), y = -2 (negative). Lies in Quadrant IV 2. Point (2, -3) x = 2 (positive), y = -3 (negative). Lies in Quadrant IV 3. Point (4, -6) x = 4 (positive), y = -6(negative). Lies in Quadrant IV 4. Point (2, -7) x = 2 (positive), y = -7 (negative). Lies in Quadrant IV Conclusion: All four points lie in Quadrant IV. Final Answer: IV quadrant.

The plane formed when the horizontal x-axis and vertical y-axis intersect perpendicularly is called the Cartesian plane. This name is derived from the mathematician René Descartes who introduced this system for locating points.

The abscissa of a point is its x-coordinate, which represents the distance from the y-axis. In the point (7, –3), the x-coordinate is 7, so the abscissa is 7.
The ordinate is –3, but it is not asked here.

The ordinate of a point is its y-coordinate. In the pair (–4, 5), the second value, which is 5, represents the ordinate or the vertical distance of the point from the x-axis on the Cartesian plane.

The coordinates (x, y) and (y, x) are only equal if both x and y have the same value. This equality means both ordered pairs represent the same point in the coordinate plane, which happens only when x equals y.

A point lies in the first quadrant if both x and y coordinates are positive. The point (3, 4) has x = 3 and y = 4, both of which are positive, so it clearly lies in the first quadrant.

Determining the Position of the Point (0, 4).
A point (x, y) is located based on its coordinates:
If x = 0, the point lies on the y-axis.
If y = 0, the point lies on the x-axis.
If both x and y are nonzero, the point is in a specific quadrant.
Given Point: (0, 4) 
The x-coordinate is 0, meaning the point lies on the y-axis.
The y-coordinate is 4 (positive), confirming its position on the positive y-axis.
Final Answer: y-axis.

In a coordinate plane, the quadrant of a point (x, y) is determined by the signs of its coordinates:
Quadrant I → (x > 0, y > 0)
Quadrant II → (x < 0, y > 0)
Quadrant III → (x < 0, y < 0) Quadrant IV → (x > 0, y < 0) Given Point: (5 -4) The x-coordinate is 5 (positive). The y-coordinate is -4 (negative). Since both x and y are negative, the point lies in Quadrant IV. Final Answer: Quadrant III.

A point on the x-axis has no vertical distance from the x-axis, so its y-coordinate, also called the ordinate, is always zero. Therefore, any such point has coordinates of the form (x, 0).

The x-axis and y-axis intersect perpendicularly and divide the Cartesian plane into four regions. These regions are called quadrants and are numbered I to IV in the anticlockwise direction from the positive x-axis.

If x = 0 and y = –4, then the point lies on the y-axis and is 4 units below the x-axis.
Therefore, the coordinates of the point are (0, –4) which is of the form (0, y).

In the second quadrant, the x-values are negative and the y-values are positive. Hence, coordinates of any point in this quadrant will always be of the form (–, +) according to the convention.

The origin is the point of intersection of the coordinate axes. Since it lies at zero distance from the y-axis, the x-coordinate or abscissa of the origin is 0. Thus, its complete coordinate pair is (0, 0).

Understanding the Abscissa of Points on the X-Axis
In a coordinate plane: The abscissa is the x-coordinate of a point (x, y).
The ordinate is the y-coordinate of a point (x, y).
Any point on the x-axis has a y-coordinate of 0, meaning its general form is (x, 0).
Conclusion:
The x-coordinate (abscissa) can be any number because points on the x-axis extend infinitely in both directions.
The y-coordinate (ordinate) is always 0 for all points on the x-axis.
Final Answer: Any number.

Understanding the Y-Coordinate of a Point on the X-Axis
In a coordinate plane:
The x-axis consists of all points where the y-coordinate is 0.
Any point on the x-axis is of the form (x,0), where x can be any number.
Conclusion: The y-coordinate of any point on the x-axis is always 0.
Final Answer: 0.

The Cartesian system, introduced by René Descartes, uses two perpendicular number lines to locate a point in the plane. It is universally accepted for coordinate geometry and uses ordered pairs (x, y) to represent positions.

In the Cartesian coordinate system, the x-coordinate or abscissa always comes first followed by the y-coordinate or ordinate. This order helps in uniquely identifying a point and avoids any confusion in representation.

The abscissa of a point is its x-coordinate. Any point on the y-axis has zero distance from the y-axis, which means its x-coordinate is zero.
Thus, the abscissa of a point on the y-axis is 0.

Since the y-coordinate is 0 and the x-coordinate is 4, the point lies on the x-axis. Any point of the form (x, 0) lies on the x-axis by definition, because it has no vertical component.

In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative. A point with coordinates of the form (+, –) meets this condition and is therefore located in the fourth quadrant of the coordinate plane.

Understanding the Sign of the X-Coordinate in the Third Quadrant
A point (x, y) lies in a specific quadrant based on the signs of its coordinates:
Quadrant I → (x > 0, y > 0)
Quadrant II → (x < 0, y > 0)
Quadrant III → (x < 0, y < 0) Quadrant IV → (x > 0, y < 0) For a Point in the Third Quadrant (III): The x-coordinate is negative (x < 0). The y-coordinate is also negative (y < 0).

Determining the Location of the Point (0, -2)
A point (x, y) is located based on its coordinates:
If x = 0, the point lies on the y-axis.
If y = 0, the point lies on the x-axis.
If both x and y are nonzero, the point is in a specific quadrant.
Given Point: (0, -2)
The x- coordinate is 0, meaning the point lies on the y-axis. 
The y-coordinate is -2, meaning it is in the negative direction of the y-axis.
Final Answer: On the negative direction of the y-axis.