Cartesian Plane MCQs Quiz | Class 9
Class IX Mathematics (Code 041) – Unit III: Coordinate Geometry. This quiz covers the Cartesian Plane, focusing on Quadrants, x-axis, y-axis, and the origin. Test your understanding of coordinate geometry concepts. Submit your answers to see your score and download the solution PDF for future reference.
Coordinate Geometry: Key Concepts
Coordinate Geometry is the branch of mathematics that allows us to locate points on a plane using an ordered pair of numbers. This system was developed by the French mathematician Rene Descartes.
1. The Cartesian Plane
The plane is formed by two perpendicular number lines intersecting at zero.
- X-axis: The horizontal number line.
- Y-axis: The vertical number line.
- Origin (O): The point of intersection of the two axes. Its coordinates are always (0, 0).
2. Quadrants and Sign Conventions
The axes divide the plane into four distinct regions called Quadrants. The sign of the coordinates depends on the quadrant in which the point lies.
| Quadrant | Nature of x | Nature of y | Sign (x, y) |
|---|---|---|---|
| Quadrant I | Positive (+) | Positive (+) | (+, +) |
| Quadrant II | Negative (-) | Positive (+) | (-, +) |
| Quadrant III | Negative (-) | Negative (-) | (-, -) |
| Quadrant IV | Positive (+) | Negative (-) | (+, -) |
3. Coordinates of a Point
A point is represented as P(x, y).
- Abscissa (x-coordinate): The perpendicular distance of the point from the y-axis.
- Ordinate (y-coordinate): The perpendicular distance of the point from the x-axis.
4. Points on Axes
- Any point on the x-axis has the form (x, 0). The ordinate is always zero.
- Any point on the y-axis has the form (0, y). The abscissa is always zero.
- The equation of the x-axis is y = 0.
- The equation of the y-axis is x = 0.
Extra Practice Questions
- What is the name of the horizontal line in the Cartesian plane? (Ans: X-axis)
- If a point lies in Quadrant III, what are the signs of its coordinates? (Ans: Both negative)
- What is the perpendicular distance of point (4, 5) from the y-axis? (Ans: 4 units)
- In which quadrant does the point (-3, 6) lie? (Ans: Quadrant II)
- What is the ordinate of the origin? (Ans: 0)
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