Coordinate Geometry MCQ Test — Class 9 CBSE

Solution:

The x-coordinate of a point refers to its horizontal position and is formally called the abscissa.

The y-coordinate of a point refers to its vertical position and is formally called the ordinate.

Therefore, the x-coordinate is the abscissa, and the y-coordinate is the ordinate.

Solution:

The x-axis divides the plane into left (negative x) and right (positive x) halves.

The y-axis divides the plane into upper (positive y) and lower (negative y) halves.

The third quadrant is formed by the intersection of the negative x-axis and the negative y-axis.

Therefore, any point in the third quadrant will have both its x-coordinate and y-coordinate as negative.

Solution:

"3 units to the left of the y-axis" means the x-coordinate (abscissa) is -3.

"4 units above the x-axis" means the y-coordinate (ordinate) is +4.

Combining these, the coordinates of point P are (-3, 4).

Solution:

For a point to lie on the x-axis, its y-coordinate must be 0 (e.g., (x, 0)).

For a point to lie on the y-axis, its x-coordinate must be 0 (e.g., (0, y)).

The given point M(0, -7) has an x-coordinate of 0 and a y-coordinate of -7.

Therefore, point M(0, -7) lies on the y-axis, not the x-axis.

Solution:

The point where the x-axis and y-axis intersect is called the origin.

At the origin, there is no displacement along the x-axis (x=0) and no displacement along the y-axis (y=0).

Therefore, the coordinates of the origin are (0, 0).

Solution:

The y-axis is a vertical line. The perpendicular distance of a point from a vertical line is determined by its horizontal displacement.

The x-coordinate (a) represents the horizontal distance of the point P(a, b) from the y-axis.

Since distance is always non-negative, we take the absolute value of the x-coordinate.

Thus, the perpendicular distance from the y-axis is |a| units.

Solution:

The y-axis is a vertical line. Any point on the y-axis has no horizontal displacement from the origin along the x-axis.

This means its x-coordinate (abscissa) must be 0.

Examples of points on the y-axis are (0, 3), (0, -5), (0, 0).

Therefore, the x-coordinate of any point on the y-axis is always zero.

Solution:

The first quadrant has (+, +) coordinates.

The second quadrant has (-, +) coordinates.

The third quadrant has (-, -) coordinates.

The fourth quadrant has (+, -) coordinates.

Given that the x-coordinate is positive and the y-coordinate is negative, the point must lie in the fourth quadrant.

Solution:

Points in the second quadrant have a negative x-coordinate and a positive y-coordinate.

We are given that point K is in the second quadrant and its y-coordinate is 6 (which is positive, consistent with the second quadrant).

Therefore, its x-coordinate must be a negative value.

Among the given options, -5 is the only negative value.

Solution:

The y-coordinate of a point represents its perpendicular distance from the x-axis.

If y = 0, it means the point has no vertical displacement from the x-axis.

Therefore, the point must lie directly on the x-axis.

Examples include (5, 0), (-2, 0), (0, 0).