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Points on the Axes and at Origin

A point on the x-axis has y-coordinate 0, a point on the y-axis has x-coordinate 0, and the origin has coordinates (0, 0).

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Student-friendly explanation

Points on axes are special because one movement is absent. On the x-axis, there is no vertical movement, so y = 0. On the y-axis, there is no horizontal movement, so x = 0. At the origin, both movements are zero.

How to write this in exams

  1. 1

    Start with the exact idea

    A point on the x-axis has y-coordinate 0, a point on the y-axis has x-coordinate 0, and the origin has coordinates (0, 0).

  2. 2

    Then show how to use it

    Check if y is 0 for x-axis. Check if x is 0 for y-axis. If both are 0, write origin.

  3. 3

    Add one concrete example

    (5, 0) lies on the x-axis, (0, -3) lies on the y-axis, and (0, 0) is the origin.

  4. 4

    Avoid this incomplete answer

    Saying (0, 9) lies in a quadrant is wrong because points with x = 0 lie on the y-axis, not inside any quadrant.

Definition

A point on the x-axis has y-coordinate 0, a point on the y-axis has x-coordinate 0, and the origin has coordinates (0, 0).

Example

(5, 0) lies on the x-axis, (0, -3) lies on the y-axis, and (0, 0) is the origin.

Rule to remember

x-axis: (a, 0); y-axis: (0, b); origin: (0, 0).

Memory hook

Zero y sits on x; zero x sits on y.

Examples and method

Worked example

Classify (7, 0), (0, 9), and (0, 0). The first lies on the x-axis, the second lies on the y-axis, and the third is the origin.

Method to apply

Check if y is 0 for x-axis. Check if x is 0 for y-axis. If both are 0, write origin.

Diagram support

A diagram may show points marked directly on axes, with labels such as (4, 0), (-2, 0), (0, 5), and (0, -3).

How CBSE asks it

Questions may ask whether a point lies on an axis, in a quadrant, or at the origin.

Avoid common mistakes

Common confusion

Students sometimes say (0, 4) lies on the x-axis because the first number is zero, but zero x means the point is on the y-axis.

Common wrong answer

Saying (0, 9) lies in a quadrant is wrong because points with x = 0 lie on the y-axis, not inside any quadrant.

Exam tip

For axis questions, remember: x-axis has y = 0, y-axis has x = 0.

Quick check

Where does the point (0, -6) lie?

The point (0, -6) lies on the y-axis because its x-coordinate is 0. It is below the origin because its y-coordinate is negative.

Answer writing and exam use

1-mark answer

A point on the x-axis has y-coordinate 0, a point on the y-axis has x-coordinate 0, and the origin has coordinates (0, 0).

2-mark answer

A point on the x-axis has y-coordinate 0, a point on the y-axis has x-coordinate 0, and the origin has coordinates (0, 0). x-axis: (a, 0); y-axis: (0, b); origin: (0, 0). (5, 0) lies on the x-axis, (0, -3) lies on the y-axis, and (0, 0) is the origin.

3-mark answer

Points on axes are special because one movement is absent. On the x-axis, there is no vertical movement, so y = 0. On the y-axis, there is no horizontal movement, so x = 0. At the origin, both movements are zero. x-axis: (a, 0); y-axis: (0, b); origin: (0, 0). Classify (7, 0), (0, 9), and (0, 0). The first lies on the x-axis, the second lies on the y-axis, and the third is the origin. Questions may ask whether a point lies on an axis, in a quadrant, or at the origin. Saying (0, 9) lies in a quadrant is wrong because points with x = 0 lie on the y-axis, not inside any quadrant.
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