medium difficulty5 min

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).

In one line: Zero y sits on x; zero x sits on y.

Practice This Concept

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1Classify (7, 0), (0, 9), and (0, 0).
2The first lies on the x-axis, the second lies on the y-axis, and the third is the origin.

Method you can reuse

1Check if y is 0 for x-axis.
2Check if x is 0 for y-axis.
3If both are 0, write origin.

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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.

Common wrong answer

Saying (0, 9) lies in a quadrant.

Why it loses marks: Points with x = 0 lie on the y-axis, not inside any quadrant.

Don't mix this up

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.

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
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
Add for 2 marks
Example: (5, 0) lies on the x-axis, (0, -3) lies on the y-axis, and (0, 0) is the origin.
3
Add for 3 marks
Points on axes are special because one movement is absent.

MCQ Quiz

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